Tears of the Kingdom's story is not at conflict with Ocarina of Time's story, nor does it retcon/contradict the rest of the series.

The Legend of Zelda timeline is a saga of many interconnected storylines across thousands and thousands of years, the series would have a three way split at the end of Ocarina of Time creating three distinct timelines; the Child Timeline, Adult Timeline, and Downfall Timeline:

The most up to date Zelda Timeline from 2017.

There have been many conversations over the years for which timeline Breath of the Wild (and therefore Tears of the Kingdom as its direct sequel) takes place on.

BOTW/TOTK have many references to all three timelines, due to this there's many theories how that could be; some believe it could be due to Hyrule Warriors or an event similar to it where any one of the timelines could have temporarily been connected to another, some believe the timelines somehow merge, and others believe in different theories.

I'm not here to give my thoughts on that topic, but to merely prove how the Zelda timeline is not ignored or retconned by TOTK, as well as show how TOTK makes an active effort to connect back to old games with its lore.

In TOTK there is the light magic wielding King Rauru who is a Zonai stated to have been the first/founding King of Hyrule.

Rauru's character profile in TOTK.

King Rauru is shown to have fought Ganondorf with Six Sages, and eventually seals him in an event known as The Imprisoning War.

Zelda fans who are very knowledgeable of the series' lore will quickly pick up on how this mirrors both OOT's story and A Link to the Past's backstory.

In OOT Link teamed up with a Hylian named Rauru, the Sage of Light, and six other Sages to defeat and seal Ganondorf:

Zelda, leader of the Seven Sages, and Link defat Ganondorf.

Rauru (Hylian) the Sage of Light, Darunia (Goron) the Sage of Fire, Ruto (Zora) the Sage of Water, Nabooru (Gerudo) the Sage of Spirit, Impa (Sheikah) the Sage of Shadow, and Saria (Kokiri) the Sage of Forest seal Ganondorf in the Evil Realm.

In ALTTP's backstory there is an event called The Imprisoning War which details how after Ganon had corrupted the Sacred Realm (Golden Land), turning it into the Dark World, many monsters began to seep out of the Sacred Realm into Hyrule. The King of Hyrule of that time would gather the Seven Sages to place a seal on the Dark World to ensure the monsters would not infest Hyrule any longer:

Description of the Imprisoning War from ALTTP (GBA) manual pages 14-15

Due to TOTK's backstory having many similarities to these events (although many differences as well) some wondered if TOTK was retconning or replacing OOT/ALTTP, as they felt there was irreconcilable differences between their stories.

I will show with definitive proof how both the events of OOT and TOTK's backstory coexist within BOTW/TOTK's lore.

However, I'd first like to debunk the theory that TOTK's backstory could take place before Skyward Sword.

We can see there are two Goddess Statues within Zonai structures: The Temple of Time and Dragonhead Island.

Temple of Time on the Great Sky Island in TOTK.

The Goddess Crest is still visible on the chest.

Dragonhead Island in TOTK.

We can confirm at least the statue in the Temple of Time was there since the backstory:

Via Memory 15 "A Master Sword in Time" in TOTK.

Zoomed in for clarity.

The Statue looks to be weathered even then, suggesting its age is much older than when we saw Goddess Statues in pristine conditions in SS:

Goddess Statue at Skyview Spring in SS HD.

The three Goddess Statues in the three Sacred Springs state the Mother Goddess Statue, which resides in the Forgotten Temple, was the model on which the rest of the Goddess Statues were based on:

Via the Side Quest "Goddess Statue of Wisdom" in TOTK.

With this we can definitively state the Goddess Statues used by the Zonai had to come after SS as the Mother Statue is implied to be the same one from the Isle of the Goddess/Sealed Grounds from SS, the Statues the Zonai used had to have been built after the Mother Statue.

Comparison of the Mother Goddess Statue in SS HD (left) and TOTK (right).

The hardest and most solid proof that shows how the stories of OOT and TOTK coexist is the mention of Nabooru and Ruto of OOT in BOTW & TOTK.

In BOTW Urbosa mentions Nabooru as a legend of the Gerudo (and a Sage in the Japanese version) and states the Divine Beast Vah Naboris was named after Nabooru:

Via the cutscene after completing Vah Naboris in BOTW.

Creating a Champion, BOTW's companion lore book, also mentions Nabooru and Ruto as being Sages, as well as the source for the names of Divine Beast Vah Naboris and Vah Ruta:

Creating a Champion page 367.

Ruto and her deeds from OOT are given an explicit recounting in both BOTW and TOTK.

In BOTW the Zora Stone Monuments written by King Dorephan would go over her exploits and state how Divine Beast Vah Ruta was named after her:

Found to the right of Zodobon Highlands and below Oren Bridge in Lanayru via BOTW.

Dorephan's daughter, Mipha, would also make a reference to Ruto in her diary:

Via BOTW's Champion's Ballad DLC. Found in the throne room in Zora's Domain.

The story of a Zora princess falling in love with a Hylian swordsman is a reference to Ruto and the Link of OOT, as seen in that game:

Ruto confessing her love to Link as both a child and adult in OOT.

In TOTK the original Zora Stone Monuments had become too weathered, and so they were re-written, this time by Sidon (Dorephan's son). Sidon would also dedicate one of the monuments to Ruto:

Found at 2876, 0031, 0124 (in-game coordinates), north of Oren Bridge in Lanayru via TOTK.

Now some may argue that the Sage of Water from TOTK's backstory could be Ruto in this story, and that the events stated in the Zora Stone Monuments and TOTK's backstory are the same events (effectively replacing OOT, rendering it as non-canon).

The Sage of Water of TOTK (left) and Ruto of OOT (right). Visually they appear radically different.

This cannot be, as the story of the Sage of Water and Ruto do not mesh together, they are clearly two separate events.

In Ruto's story it is written how a "wicked man" (Ganondorf) came to rule Hyrule, and that Ruto worked with the Princess of Hyrule and the Hero of Legend to save Hyrule.

Let's go over how this does not line up with the events depicted in TOTK's backstory and how Ruto and the Sage of Water are separate people.

In order for the "TOTK's backstory & Ruto's story are the same event" theory to work, we would need to identify who the Princess of Hyrule and Hero of Legend are in Ruto's story.

While some may think it's obvious the time traveling Zelda would fit as the "Princess of Hyrule" as she's even called "Princess Zelda" by Sonia and Rauru's nursemaid, this doesn't work when you remember Sonia states Zelda would be known as a "distant relative":

Via Memory 3 "Where Am I?" in TOTK.

Due to Sonia, Zelda would be known as a foreign princess of a kingdom separate from Hyrule. Via the Ancient Tablet "The Foreign Princess" interpreted by Wortsworth in Kakariko Village in TOTK.

Whilst Zelda would still be known as a Princess, she was not known as the Princess of Hyrule in TOTK's backstory. Zelda was mostly just known as the Sage of Time.

The identity of the Hero of Legend would be even harder to find, as the only person who could even remotely fit the role of "Hero of Legend" in this story would be Rauru, as he was the one who actually sealed Ganondorf. The issue is that Rauru is exclusively referred to as "King Rauru" or "Founding King" in the present, at no point is he even referred to as a hero, let alone Hero of Legend. Even Purah only vaguely remembered him as the "first King of Hyrule".

Something worth mentioning is the fact Ruto in BOTW/TOTK is referred to as "strong willed" and "lively", much like how she was depicted in OOT.

In the Japanese version of TOTK (based on Google Lens translation) she appears to be referred to as "tomboyish", something which she is explicitly referred to as in OOT:

Google Lens translation of a sentence from the aforementioned Zora Stone Monument "Learnings of the Zora, Part Two" in TOTK.

Via dialogue with a Zora in Zora's Domain after finding Ruto in OOT.

OOT manual page 8.

The Sage of Water in TOTK was never shown to have any of these traits, as she was depicted as being much more quiet and reserved. This further differentiates her from Ruto.

I can state definitively: The Sage of Water and Ruto are separate people.

With this we can ascertain that within TOTK the events of OOT are a canon event which happens separate from its backstory.

Adding further credibility to this is the Goron Stone Memorial found in Goron City in BOTW & TOTK:

In Goron City via TOTK.

This memorial depicts statues of Daruk from BOTW, The Goron Elder's Son & Darmani III from Majora's Mask, and Gor Coron from Twilight Princess:

Up close comparison with the Goron Stone Memorial.

Darmani III is from Termina and has a Hyrulean counterpart found in OOT, Darunia. Due to the fact Darmani III (and the others in the memorial) retains his design from MM, we can assume Darunia should also retain his design. With this assumption we can rule out the possibility the Sage of Fire of TOTK being Darunia as he appears significantly more like Daruk than Darunia, such as the hair on their forearms, their muscular abs, arm/leg length, etc:

Darunia of OOT (left), Sage of Fire of TOTK (middle), & Daruk of BOTW (right).

Like Ruto and the Sage of Water this would confirm Darunia and the Sage of Fire are separate people, further confirming the events of OOT coexist as a separate event to TOTK's backstory in TOTK's history.

At this point many may wonder:

"In TOTK Rauru is called the first King of Hyrule, and the establishment of the Kingdom of Hyrule in the official timeline is stated to be after Skyward Sword but before OOT. If that's the case, then how does OOT fit into these events if it is after the establishment of Hyrule, but Ganondorf is supposed to be sealed under Hyrule Castle?"

Stone monument found in the Royal Hidden Passage under Hyrule Castle in TOTK.

Via Ganondorf's character profile in TOTK.

The best conclusion I've come to, which doesn't cause any conflict with previously established lore, is that the establishment of Hyrule by Sonia and Rauru is a separate one after the first establishment which was before OOT.

There are many issues when taking "Rauru and Sonia are the first King and Queen of Hyrule who founded the kingdom" literally and at face value.

One such issue is the aforementioned fact Ganondorf in TOTK had been sealed under Hyrule Castle for 10,000+ years. An example of how this shouldn't work with a past Zelda game is in OOT where Ganondorf destroyed Hyrule Castle and built his own over the remains of Hyrule Castle. If the Castle acted as a seal, then couldn't TOTK Ganondorf have awoken then?

Another issue would be the Gerudo's ears. In all games prior to BOTW the Gerudo had rounded ears, unlike the Hylian's pointed ears:

Nabooru from OOT (rounded ears).

In BOTW & TOTK they have pointed ears:

Isha, Riju, and Cara via TOTK (pointed ears).

This difference is noted in Creating a Champion which gives two possible explanations for this:

Creating a Champion page 401.

In TOTK's backstory you can see the Gerudo women have pointed ears:

Via Memory 6 "The Gerudo Assault" in TOTK. 

If TOTK's backstory takes place before OOT, why are their ears pointed then but get rounded in OOT, then return to being pointed in BOTW? This would be especially odd if the reason for pointed ears was from mixed racing.

Another issue would be the existence of the Rito. The Sage of Wind in TOTK's backstory is a Rito. The Rito are stated to be evolved descendants of the Zora as shown in The Wind Waker. If TOTK's backstory is before OOT, then how do the Rito exist? They shouldn't exist back in that era. Regardless of which timeline BOTW/TOTK take place on, the Rito should not exist in an era during or before OOT.

All of these issues are non-existent under the re-founding theory.

Under this theory we will assume that before the time of Sonia, all the past games takes place (whichever timeline), then many years later for some reason the Kingdom of Hyrule collapses and is all but forgotten. Later, the Zonai come down and Rauru and Sonia established the "new" Kingdom of Hyrule, and unbeknownst to them a Kingdom of Hyrule had already existed in the past.

Worth noting is the fact Ganondorf states Rauru took a "Hyrulean" woman as a wife, Sonia, who was a "Hylian" priestess before marriage:

Via Memory 7 "A Show of Fealty" in TOTK.

Via the Ancient Tablet "The Strong Queen and Receptive King" original text and Wortsworth's interpretation. Note the original text states "Hylian preesterresse".

Although an established kingdom of Hyrule didn't exist at the time, the names "Hyrule" and "Hylian" did. This implies though knowledge of the previous kingdom didn't survive to this era, the names of that kingdom and its people did.

For comparison in SS, Hyrule was not a founded kingdom, in fact "Hyrule" is not used once in that game. Instead, the land that will become Hyrule was just known as "the surface":

Via the final cutscene in SS HD.

The theory of the re-founding is not some wild fan theory, but actually based on canon lore.

We've actually seen an example of this happening in the Adult Timeline, where Ganondorf broke from his seal and terrorized Hyrule, which prompted the Goddesses to flood the entire lands and washed away the Kingdom of Hyrule:

King Daphnes Nohansen Hyrule explains how Hyrule was washed away by the gods. Via WW HD.

Life would continue on the Great Sea, and after WW, Tetra and Link would eventually find a new land to establish a new kingdom called New Hyrule.

The Downfall Timeline is another example of how decayed the Kingdom of Hyrule can become.

In ALTTP we learn about the Hylia bloodline becoming thin, and how even the Maidens didn't retain the powers of the Seven Sages despite being their descendants:

Via the cutscene after saving the Maiden in the Ice Palace in ALTTP (GBA).

ALTTP takes place in an era where Hyrule was one Kingdom, as stated on its Japanese box:

Japanese original (top) and Google Lens translation (bottom).

Zelda II's backstory also mentions Hyrule used to be one country:

Zelda II: The Adventure of Link manual page 6.

By the time of Zelda 1 & 2 the Kingdom has been reduced, now known as a "little" Kingdom. It's also stated Hyrule was on the road to ruin, and that circumstances did not look very good:

The Legend of Zelda manual pages 3-4.

Zelda II: The Adventure of Link manual pages 3-4.

We would also see in Zelda 1 how some had to resort to living in caves, likely due to the state of Hyrule during that era:

The Legend of Zelda  manual page 6.

These examples are canon evidence the Kingdom of Hyrule does not always last in a state of flourishment, and that something similar could have happened to the Kingdom before the time of Sonia.

With this theory accepted, there is no longer an issue with the Gerudo's ears, Hyrule Castle needing to stay intact to be a seal, or the Rito's existence in an era before/during OOT.

This theory is also backed up by Creating a Champion where it goes over the timeline. It recounts the events of OOT and refers to it taking place in the Era of Myth. It goes over how due to Hyrule having several periods of prosperity and decline it's impossible to tell what events are historical facts and what's mere fairy tale:

Creating a Champion page 361.

It also goes over how much of the documentation of the past was lost in the Great Calamity:

Creating a Champion page 361.

Also stated is how the documentation of the past varies by race, for example it notes how the Zora have plenty of documents, but the Rito don't (this can account for why Ruto was so well remembered, while others of the past may not have been):

Creating a Champion page 363.

After the Era of Myth comes the Era of Prosperity, then finally comes the events of 10,000 years ago (the Great Calamity):

Creating a Champion page 360.

The era of Sonia and Rauru would come after the Era of Myth and during the Era of Prosperity.

One thing I'd like to point out is the fact in Hyrule Historia (and still on the official Zelda website) the Era of Prosperity is also where the Establishment of the Kingdom of Hyrule takes place. So within Zelda lore at the time of BOTW there was two places referred to as "Era of Prosperity", one after SS and before Minish Cap, and one long after OOT but before the events of 10,000 years ago (in BOTW). It would be interesting to think of "Era of Prosperity" as the indicator for the establishment of Hyrule's Kingdom.

Hyrule Historia page 77.

Hyrule Historia page 69.

Via Zelda.com

With this we could look at it as this:

-Pre-OOT "original" Era of Prosperity: Hyrule Kingdom is established.

-Some time long after OOT: Hyrule goes through a great decline.

-Pre-BOTW "new" Era of Prosperity: Hyrule Kingdom is established by Sonia and Rauru.

The idea Hyrule was re-founded by Rauru and Sonia is something I feel also fits the themes and narrative of the series. Within the Zelda lore there is a cycle as stated in SS, a cycle of Demise's hatred being forever reborn, as well as there always being a Link and Zelda:

Via cutscene after defeating Demise in SS HD.

This concept was also implied by Ganondorf at the end of TP:

Via cutscene after defeating Ganondorf in TP HD.

A synonym to "cycle" can be "circle", "loop", or "ring". In TOTK loops are a large part of its imagery and themes, such as its main logo which depicts two dragons in a loop, much like the ouroboros:

Various places rings or circles are depicted in TOTK. Note how even the mural depicting Rauru and Sonia has their hands forming a loop.

In TOTK Garshon comments on the Ring Ruins in Kakariko Village, and makes note of their eternal feeling:

Near the east side of Dueling Peaks in TOTK.

The idea that rings can represent something eternal connects with their synonym "loop", which in turn connects to the series' theme of an endless cycle with Demise's curse, that there will always be a "demon king" for Link and Zelda to battle.

Perhaps this is why TOTK parallels aspects of OOT (& ALTTP):

Ganondorf kneeling before the King of Hyrule. TOTK (left) & OOT 3D (right).

Maybe it's not an indication of TOTK replacing OOT, but merely to represent this as being another cycle, and the OOT parallel is to convey the cycle beginning again and merely repeating history, as a cycle would.

Something I feel which adds to the re-founding theory is the fact the Triforce is not in BOTW, TOTK, or their backstories. To explain, a dev wrote in Creating a Champion that Boars, Dragons, and Owls are all imagery the Zonai used in their architecture and it was meant to show the Zonai's ancient interpretation of the Triforce:

Creating a Champion page 342.

Boar, Dragon, and Owl statues found in Faron and Thyphlo Ruins in BOTW/TOTK.

It's also stated in Creating a Champion that, outside of the crest on Zelda's hand, there is no real knowledge of the Triforce in the era of BOTW:

Creating a Champion page 388.

The only ones who seemed to have some knowledge of the Triforce were some of the Sheikah Monks of 10,000 years ago who received divine messages from the Goddess Hylia:

Creating a Champion page 371.

This helps the re-founding theory in that the facts of the Triforce are gone in both the era of Sonia as well as the modern era. It feels as if information of the past was truly lost, since something as prominent as the Triforce has been all but forgotten. This can strengthen the belief the people of Sonia's era truly were unaware of the Kingdom of Hyrule existing before them.

The lack of the Triforce also explains why Ganondorf made no attempt to steal it in TOTK, and instead sought after the Secret Stones as the means to become the Demon King.

This plot for Ganondorf is also similar to Four Swords Adventures, where it too had no mention of the Triforce and Ganondorf instead sought another means to become the "Demon King", in this case he used the Trident to enhance his demonic powers.

FSA also helps explain why the Ganondorf of TOTK would have no memories of the previous games, as it shows how a new Ganondorf was born into the Gerudo with no apparent knowledge of his past self:

A Gerudo recounts the Ganondorf of FSA's past to Link.

Zelda refers to the Ganondorf of FSA as being "reborn".

This is the same situation TOTK would have, where a new Ganondorf was born. The only difference would be the Zelda of FSA would have knowledge of records of the past Ganon.

On the topic of "multiple" Ganondorfs existing in Hyrule's history, the Ganondorf of OOT is directly mentioned in BOTW, where the Hyrule Compendium description for Calamity Ganon states it was once known as "Great King of Evil" ("Great Demon King" in Japanese), this is the same description for the Ganondorf of OOT:

English (left) & Japanese (right). Pre-Boss fight description for Ganondorf in OOT (top) & Hyrule Compendium entry for Calamity Ganon in BOTW (bottom).

While the Ganondorf of TOTK is known as "Demon King" in both the English and Japanese versions, he's never referred to as "Great" Demon King, not even in the Japanese version (as far as I could tell):

A collage of various places "Demon King" is used in the Japanese version of TOTK. No where does it appear "Great Demon King" is used.

Explanation for the characters used to write "Demon King" & "Great Demon King" in Japanese as it relates to the Zelda series.

Comparison of OOT & BOTW's use of "Great Demon King" to TOTK's "Demon King". Note the lack of "大" in TOTK.

The moniker of "Great", whether it's for the English version of "Great King of Evil" or the Japanese version of "Great Demon King", is missing from the Ganondorf of TOTK. We can surmise this means the Ganondorf of OOT, who uses "Great" in his title, is a separate Ganondorf that did indeed exist in BOTW/TOTK's history.

Some may point out the fact Calamity Ganon is said to have existed from the manifested hatred of the Demon King Ganondorf of TOTK and wonder how its Compendium description can still work as a reference to OOT Ganondorf:

Via dialogue with Impa when she returns to Kakariko Village in TOTK.

This was first set up to be the case in BOTW when King Rhoam states the "Demon King" was born in Hyrule, before he transformed into Malice:

Via the cutscene when King Rhoam reveals himself in BOTW.

This still works, as much like how Zelda in FSA referred to that Ganon as "ancient demon reborn", same thing would apply here. Ganon is Ganon, regardless if he's reborn in a new body or not. Same entity, different incarnation.

Just how FSA Ganon is attributed the feats of the original OOT Ganon, the same can apply here. However any new Ganon manifests itself, it was always once the "Great King of Evil/Great Demon King" of OOT.

So although Calamity Ganon spawned from the "Demon King" Ganondorf of TOTK, it has its roots all the way back to the original "Great King of Evil/Great Demon King" Ganondorf of OOT, and therefore is how it was "once known as" Great King of Evil/Great Demon King.

Something else I feel adds to the re-founding theory is the Gerudo Shield. In BOTW & TOTK the Gerudo Shield is described as having been changed over time to adapt to the Gerudo's sword & shield fighting style:

Gerudo Shield Hyrule Compendium entry via TOTK.

Interestingly, the Gerudo of TOTK's backstory also wielded this shield alongside swords:

Several Gerudo behind Ganondorf wield the Gerudo Shield. Via Memory 6 "The Gerudo Assault" in TOTK.

Zoomed in.

This means the Gerudo Shield had its design changed before Sonia's era, which also means there was a time before this when the Gerudo hadn't adopted the sword & shield fighting style.

Looking at the past games' depiction of the Gerudo, we see they didn't use the sword & shield fighting style. An example would be in OOT where they used a spear or two swords, but not a shield:

Two Gerudo from OOT 3D.

This seems to imply that games like OOT do indeed take place before TOTK's backstory, as it shows the era in which the Gerudo hadn't yet adopted the sword & shield fighting style (which is mentioned, but not depicted, in BOTW and TOTK).

In BOTW there were many references to past games, whether it was in the names of locations or through certain items obtained via amiibo. At the time some had questioned the canonicity of these, wondering if they were merely references, especially since they lacked a Hyrule Compendium entry.

I would like to point out how in BOTW the mentions of both Nabooru and Ruto are not mere references, but spoken of from main characters, and they give backstory to the world. Urbosa mentions Nabooru directly as being the inspiration for Naboris' name, Dorephan writes about Ruto in a Zora Stone Monument and mentioned she was the inspiration for Vah Ruta's name, and Mipha writes about "a Zora Princess who loved a Hylian" (depicted in OOT with Ruto becoming Link's "fiance") in her diary in the Champion's Ballad DLC. In TOTK Sidon writes about Ruto in a Zora Stone Monument and how he's inspired by her, as well as revealing he is her descendant. In both BOTW and TOTK these Zora Stone Monuments are crucial to the lore, world building, and character development to the Zora, especially in TOTK as it relates to Sidon and Yona.

Basically what this means is these references to Nabooru and (especially) Ruto cannot be written off as "questionably canon references", as they are directly tied to the main story and world building of BOTW & TOTK.

Additionally, I'd like to point out how all of the items that used to be exclusive to amiibo in BOTW are now gotten normally in the world of TOTK (without needing amiibo). Some of these items are even tied to quests.

Due to this, I feel they are now fair game to talk about when discussing canon.

Most of these items can be found via Old Maps in TOTK. These maps are all found inside Zonai Treasure Chests on the Sky Islands:

Via the "Key Items" page in TOTK. These maps are not used only for the previously amiibo exclusive items, but also new outfits such as the Miner's outfit.

Various items and their Hyrule Compendium descriptions found in TOTK which are from Zelda 1, OOT, MM, & WW.

A few items have had their descriptions re-written, such as the Twilight Bow, known in TOTK as Dusk Bow, which is found at the very top of Hyrule Castle. There is a new line in its description which mentioned it has been passed down though the Royal Family of Hyrule:

BOTW.

TOTK.

This re-written description tells me it was intentional to create a stronger connection to Twilight Princess as being a canon event in TOTK's history. If the devs wanted it to just be a non-canon reference, as some believed it was in BOTW, then why re-write it to put extra emphasis on its historical relevance?

Another thing to consider is the fact the devs wanted TOTK to be accessible to any newcomers playing a Zelda game for the first time:

Ask the Developer Vol. 9, The Legend of Zelda: Tears of the Kingdom—Part 1.

If we think on it from their perspective, wouldn't they just take the Dusk Bow as being a canonical weapon passed down in the Royal Family? It wouldn't be "just a reference" to them, to them it would be taken as a unique item which adds to the world building of TOTK, and again, would be accepted as completely canon.

Another item in TOTK that was an amiibo exclusive in BOTW is the Sword of the Six Sages, known in TOTK as the Dusk Sword.

This sword is found in the Thyphlo Ruins after completing a series of side adventures that relate to the Sages of Wind, Lightning, Water, and Fire:

Stone monument found in Thyphlo Ruins.

TOTK.

BOTW.

You can find a clue to the location of the Dusk Sword in the Sage Temple Ruins where a stone monument states the sword used to reside there before it was moved to the Thyphlo Ruins, and that it was in honor of the Sages:

The changing of the name Sword of the Six Sages to Dusk Sword seems to be a consistent thing in TOTK where many previous references to Sages that were in BOTW are no longer in TOTK. A list of a few things that were noted as a Sage in BOTW were Ruto, Satori (said to be a reincarnation of a Sage), and the Sword of the Six Sages:

A list of the various times "Sage" was used in BOTW that's not in TOTK.

My hypothesis is the devs didn't want to confuse new players with references to other Sages that have nothing to do with TOTK's plot, because if the Dusk Sword, for example, was called the Sword of the Six Sages it may be confusing to new players how it relates to TOTK's Sages or why its sheath has the Gerudo emblem:

TOTK (left) & TP (right) via Arts and Artifacts page 276.

They may wonder why the Sage of Lightning (the Gerudo Sage), didn't wield it (since it has the Gerudo emblem) or why it wasn't in the backstory whatsoever.

(This "we can't reference other Sages of past games to not confuse new players of TOTK" theory also leads further credence to Ruto being separate from the Sage of Water, because she was called a Sage in BOTW but not in TOTK. This leads me to believe the devs didn't want Ruto called a Sage in TOTK so new players wouldn't wonder why there was this Sage named Ruto that had nothing to do with the plot of TOTK)

That being said, now the only way to make contextualized sense of the Dusk Sword requires one to have knowledge of the previous games in the series, specifically TP. Why was this sword used to honor the Sages in TOTK? Well it's because this is the sword the Ancient Sages of TP used, specifically being the exact blade used in the (failed) execution of Ganondorf:

Ganondorf kills an Ancient Sage after the Sword of the Six Sages failed to kill him. Via TP HD.

The Hylian Shield is also an item which has an explicit reference to a previous Hero. We can ascertain via it's design it is the same one used in SS. It's clear it's the same shield from that game, expect it has chips in its metal, showing its damage/age from its use in/since SS:

Hyrule Compendium entry for the Hylian Shield in TOTK.

Image I made to compare the Hylian Shields in the series.

For those who may not recall, the Hylian Shield was never BOTW/TOTK Link's primary shield, as he never even had it during the 100 years ago backstory to BOTW. Never was this Link marketed in artwork as wielding it, unlike previous games like OOT, TP, SS, etc:

Previous games marketed Link with the Hylian Shield.

BOTW/TOTK doesn't feature the Hylian Shield in any of its artworks for Link.

This means the intent of the Hylian Shield in BOTW/TOTK is to show how it belonged to a previous Link in the series, specifically SS Link.

In TOTK Fin even comments on it as being a legendary shield when you talk to him with the it equipped:

Found at Selmie's Spot in Hebra. Via TOTK.

Like many of the aforementioned items, in TOTK there are outfits based on the past Links of the series which used to be amiibo exclusive in BOTW, which again are now gotten normally and not tied to amiibo.

Since even in BOTW the Dark Link outfit wasn't tied to amiibo, I will start with it.

This outfit is based on Dark Link from OOT, and is found via Kilton in BOTW and via a Bargainer Statue in TOTK. This outfit is said to be a replica of the green one a legendary hero wore (it's the exact model for OOT Link's tunic) an obvious reference to OOT Link:

BOTW.

TOTK.

OOT Link's outfit in BOTW/TOTK for comparison.

What's interesting about the other Link (or Hero) outfits, is they help effectively "confirm" the Ancient Hero Aspect (which is said to contain the spirit of a hero who saved Hyrule in the past) from TOTK represents the Hero of 10,000 years ago from BOTW:

Comparison of the Ancient Hero Aspect (left) and the Hero of 10,000 years ago (right) depicted in the tapestry in Kakariko Village. Note their similar red hair, grey/green skin, shoulder markings, long snout, dark eyes, etc.

When upgraded, the Ancient Hero Aspect gives the set bonus "Master Sword Beam Up" just like the Tunic of the Wild (the tunic original to BOTW, not based on a previous game). This suggests the Ancient Hero wielded the Master Sword:

Aside from those connections between the Ancient Hero and the Hero of 10,000 years ago, the fact the outfit is sorted with the other Link outfits in the menu seems to suggest it too is a "Link (or Hero)" outfit. Whether the inventory is sorted as "Set" or "Part", the Ancient Hero Aspect is immediately after all the other Link outfits:

Outfits sorted to "Set".

Outfits sorted to "Part".

This seems to imply the Ancient Hero and the Hero of 10,000 years ago are one and the same.

Perhaps the fact the Ancient Hero Aspect is after all the previous games' Links suggests those Links came before the Ancient Hero? If so, then this again confirms the previous games canonically exist within TOTK's history.

Many other outfits of past games, including some previously locked to amiibo, are found via finding Misko the Bandit's hidden treasures. Misko's treasures are hidden in caves which are marked with their unique insignia, and the actual treasure chests are found in uniquely designed shrines:

Misko's unique insignia and shrine. Via Cephla Lake Cave in TOTK.

Misko is a character spoken of in BOTW/TOTK's past, who now has a large following of people looking for their treasure. Many treasure hunters in TOTK are looking for Misko's treasures, including the Cece fans:

Cece fans discuss Misko's treasure. Via Hateno Village in TOTK.

Domidak and Prissen search for Misko's treasure in TOTK.

Misko will often leave stone tablets or letters in bottles to give clues to their hidden treasure. In these clues Misko sometimes gives a bit of backstory to the treasure, which connects to past games:

Termina of MM is likely one of the "strange lands" Misko references, as it's where the Fierce Deity outfit & sword originates. 

Another notable connection to a past game is the quests involving the three Lomei Labyrinths. These three quests are given by the Rulers of Boars, Dragons, and Owls. 

These quests eventually lead to the Rulers giving Link a piece of the Evil Spirit Armor, known as the Phantom Ganon Armor in BOTW (perhaps renamed to not confuse newcomers with TOTK's own Phantom Ganon boss). The fact this outfit is tied to such unique quests, I feel these should also be taken as unquestionably canon and not just "some reference", especially since there are journals written by Calip (an NPC related to the main quest) in each labyrinth where he goes over his and Tauro's (another main character) attempts to uncover the Labyrinths' secrets.

The Rulers mention the Evil Spirit Armor is "wreathed in otherworldly evil":

This is an interesting detail, as in OOT after Link defeats Phantom Ganon, Ganondorf comments on the Phantom's inability to defeat Link and as punishment he sends it to the place between dimensions:

Via the cutscene in OOT 3D after defeating Phantom Ganon.

This could be where the "otherworldly" comment by the Rulers comes from. Perhaps Phantom Ganon was stuck in that "place between dimensions" for so long it's essence has left the armor?

Another interesting detail is the fact this armor was said to have been "hidden away since days of old", and is located in a Lomei Depths Labyrinth, which is of Zonai design. Obtaining the armor requires the defeat of a Flux Construct III.

Flux Construct III Hyrule Compendium entry in TOTK.

The Constructs were creations of Mineru, who was a Zonai and Rauru's sister:

Via the Ancient Stone Tablet "The Researcher Mineru". Interpreted by Wortsworth (left) & original text (right).

After the Imprisoning War, Mineru places her spirit inside the Purah Pad and awaits the day Link would need her 10,000+ years later.

Since the Evil Spirit outfit was hidden away in the Labyrinths, we can assume the Flux Construct IIIs acted as guards, and by nature of Constructs not existing until Mineru created them, it means the Evil Spirit outfit existed before it was hidden in the Labyrinths, before the Constructs were created, before Mineru came down to Hyrule with her brother, before the establishment of the Kingdom by Rauru and Sonia.

This further strengthens the re-founding theory, as OOT had to take place before the Evil Spirit (Phantom Ganon) outfit was placed in the Lomei Depths Labyrinths and before Mineru could have created the Flux Construct IIIs in order for them to have stood guard.

All complete outfit sets in TOTK, including those based on previous games, can be reviewed by Cece after completing "The Mayoral Election" quest in Hateno Village. I feel this even further solidifies their canonicity in TOTK.

Using the Hero of Twilight outfit, this is an example of Cece reviewing a complete set in TOTK.

Another solid connection to OOT in TOTK is the large fish sculpture in Zora's Domain being based on Jabu-Jabu that first appeared in BOTW:

Via Zora's Domain in TOTK.

Creating a Champion page 276.

Jabu-Jabu already had an implicit mention in BOTW where it was stated Ruto "was an attendant to the Zora patron deity", Jabu-Jabu is called the patron deity of the Zora in OOT.

A dev quote in Creating a Champion would state the large statue in Zora's Domain was based on Jabu-Jabu of past games and that it was to show the Zora's reverence of him:

Creating a Champion page 274.

In TOTK there is a quest to obtain the Vah Ruta Divine Helm where Sidon states he found a clue to it's location by looking through books related to the Zora Royal Family, where one mentions a treasure underneath the statue of the "The great fish. The eternal guardian":

Via the Secret Treasure under the Great Fish quest in TOTK.

As hinted by the passage Sidon found, the treasure, the Vah Ruta Divine Helm, was found under the great fish statue in Zora's Domain. This is a clear reference to Jabu-Jabu, reaffirming what Creating a Champion stated.

In BOTW the Master Sword is said to contain a voice, and we see this voice communicate with Zelda (we also see this again in TOTK). It is the same sound effect used in SS when Fi speaks:

Comparison of Fi's blue glow and sound effects when she talks in SS HD, BOTW, and TOTK.

This clearly is meant to show how Fi's essence still resides in the Master Sword, even after all this time.

TOTK goes even further, where the Great Deku Tree states the sword was created by a goddess:

Via Memory 1 "The Master Sword's Power" in TOTK.

In SS we learn the Master Sword originally was the Goddess Sword created by the Goddess Hylia.

Zelda in TOTK refers to the Master Sword as "she" and "her", again this clearly references Fi of SS:

Via Memory 18 "Zelda's Wish" in TOTK.

This also reaffirms what was said in Creating a Champion:

Via Creating a Champion page 388.

Interestingly, after completing "The Mother Goddess Statue" quest in TOTK, you are gifted the White Sword of the Sky by the Mother Goddess Statue:

Hyrule Compendium entry for the White Sword of the Sky in TOTK.

This is the Goddess Sword from SS in its 2nd phase (before becoming the Master Sword in its 4th phase):

Comparison of all phases of the Goddess Sword/Master Sword, from left to right: Goddess Sword, Goddess Longsword, Goddess White Sword, Master Sword, True Master Sword. Via Zelda Encyclopedia page 83.

In SS, you had to forge the Goddess Sword in the sacred flames of Nayru, Din, and Farore for it to become the Master Sword.

Zelda Encyclopedia page 83.

In TOTK, in order to complete "The Mother Goddess Statue" quest you have to offer a claw from the immortal dragons Naydra, Dinraal, and Farosh to the Goddess Statues of Wisdom, Power, and Courage located at the Springs of Wisdom, Power, and Courage so they can restore the Mother Goddess Statue:

Via TOTK.

Via TOTK.

Perhaps this was enough power to create a 2nd phase Goddess Sword, but not enough to create another Master Sword?

I know there's more I could cover, but I will just go over one more thing, and since this next reference to past games requires amiibo (and may not be seen as "legitimate" by some), I've saved it for last.

In BOTW & TOTK there are many stables across Hyrule, and while not stated in-game, Creating a Champion shows their company name is Epona Co., named after the horse used by a "legendary hero" (Link of a previous game):

Artwork of Link riding Epona for OOT 3D.

TOTK in-game logo (top) & Creating a Champion page 337 (bottom).

Obtaining Epona in BOTW & TOTK requires a Link amiibo (Smash or Twilight Princess). When registering Epona, the stable employees will comment on her being a legendary horse, and are adamant about not changing her name:

Via TOTK.

With all that I've written, I believe I have proven how TOTK does not do away with the timeline nor retcons OOT/ALTTP out of canon.

I want to say thank you to anyone who read to the end, I know it was a lot.

I also want to say that all I wrote about were conclusions I came to on my own during/after the 250+ hours I put into playing through TOTK. I never looked at any one else's theories, as I was actively avoiding any spoilers. That said, the only one thing I did learn from someone was on Reddit about the bit about Phantom Ganon being sent to the place between dimensions in OOT (this was after I had already gotten the Evil Spirit Armor). I would credit them if I could remember the post.

Most of the images in this post I manually took either via screenshots from BOTW, TOTK, & SS HD, or pictures from my copies of Creating a Champion, Hyrule Historia, Encyclopedia, and Arts & Artifacts. Beyond those images, I made screenshots via other websites or videos (which I credited via links).

Thank you again for reading.

I hope you enjoy the Zelda series as much as I do!

Goodbye 👋