I am personally a fan of the idea that the past of Tears of the Kingdom is the time before Skyward Sword. To this end, I went through both games, comparing features of the structures. I originally grabbed screenshots from both games, with the intent of posting comparisons. Instead, to make this as spoiler free, and as accessible as possible, I will only provide pictures from Skyward Sword, and will try to speak about Tears of the Kingdom vaguely enough to not spoil anything, while hopefully providing enough detail for each of you to know what I am even talking about.
Firstly, I would like to start with this image:
These designs are found around the goddess statue, in the sealed grounds, and a few other places, throughout Skyward Sword. These patterns are also found in the recent games, Breath of the Wild and Tears of the Kingdom, on many structures throughout Hyrule, such as the Lanayru Promenade. It would be easy for Hyrulian builders to replicate these features, and maintain them. To be clear, this does not suggest that the current structures, such as the promenade, were built by Zonai, as well. It does suggest that the society built after Skyward Sword has survived until Tears of the Kingdom. The sealed grounds, and the fallen Goddess statue would have been easily accessed by early Hyrulian builders. This means that there was only one Hyrule between the two games.
This continuation is further supported by the circuitry designs found on ancient Shiekah productions, found mostly in Breath of the Wild, but can also be found in Tears of the Kingdom. The designs are also seen in Skyward Sword. One example, I will present here:
But, the design is also seen on the portals of time, one of the boss keys, and on the sealing spike, all in Skyward Sword. There is at least one Shiekah in the past of Skyward Sword, so there is room for debate if all of this tech was created by Shiekah, from the beginning, or if this is one aspect they latched onto while reverse engineering Zonai technology. This gets even muddier when taking in the theory of time traveling Shiekah, originating from the future. Either way, this also indicates a continuum between the games.
Another connection, but even more vague, is the ship from Skyward Sword:
This ship has the ability to go invisible, which does not, as I am aware, carry over, but the color scheme, and patterns should look familiar, if you work through the main story of Tears of the Kingdom. Interestingly, the intended crew for this ship, in the picture, are robotic lifeforms, so it makes since that there is no galley.
In the ship, there is also an interesting symbol, on the walls:
Many have already suggested this to be a Zonai swirl, but the exact mark, minus the V shaped wings on either side, can be found on the bird (possibly Rito) like statues in the Thyphlo Ruins. I've always associated these swirls with the Kokiri, to be honest, but the connection to the Rito is interesting.
With the general connections, indicating a casual continuation, lets move onto the Zonai ruins we saw in Breath of the Wild. A major theme in these ruins were the dragon shapes. Huge square blocks were shaped to look like the Asian style dragon, and some carvings look like dragons moving back and forth, in a square shaped pattern. This carving can easily be found in the Thyphlo ruins, on some pillars, in Tears of the Kingdom. Then there are also some structures, in the depths, that have similar square shaped Asian style dragons, such as what are commonly called elevators. That easily connects with this key, from Skyward sword:
This Door:
And, this gate:
The gate style looks familiar. Here is another, from the same area, that is freestanding:
Many Zonai structures we find in Tears of the Kingdom have a similar basic building structure; namely the two pillars, topped with a header that runs past the two pillars. Many can be found freestanding, and not all with the same dealing. An example of this, in Tears of the Kingdom, is below the Death Mountain area. It is also important to point out that not all Zonai structures are shown to have this type of archway doorways. At least one round topped door is seen in one of the memories.
The door, in that memory is not the focus of the scene, so details beyond square patterns, and a lotus pattern are not easy to see. Though lotus patterns are also a common theme. In Tears of the Kingdom, they can be found in many places. I don't think the Zonai lights are meant to be lotus flowers, but bright blooms. The pasterns I am talking about can often be found in the little round device staging pads. Skyward Sword is full of Lotus shapes. Here are just a few:
This one being similar to the door in the memory I had mentioned.
And, this skylight being almost the exact same pattern as the device staging pads.
There are many more examples, and I encourage you to go back, and check out the game for yourself, but I need to keep the ideas moving. (I have also apparently reached the maximum ten pictures, so I will post the rest in a reply, as soon as I post this.) See, similar to the flower petals are designs that could be feathers, or scales. They can be found in many Zonai structures, adorning the walls, such as in the shrines. The most interesting example I found, in Skyward Sword, is found on the back of the head of the figure in the Ancient Cistern. I also see the cistern as a possible, in universe, prototype for the light shrines, in that it connects to the depths, and appears to be purifying the water. I also think this temple may reference the Zora and Rito existing before Skyward Sword, and I plan on making a deeper dive into that, at a later date, as that topic is bound to contain far more spoilers. Long story short, I believe the Cistern predates the light shrines, and even led to their eventual construction. Just look at the space below:
Plus, many of the structures feature round elements, that protrude out from the structure, some of which are even intended to be jumped from:
There is also the artwork detailing the history, presented in the beginning of Tears of the Kingdom. This style is called relief. While we don't see the same exact thing for Skyward Sword's prologue, looking more like paint on stone, We do see reliefs, providing information. Many of these reliefs utilize hard angles, just like the ones in Tears of the Kingdom. the differences between them are indicative of different artists using the same techniques.
Next are the glowing letters, related to holy power. If you have completed a light shrine, you have seen these. They are also in memories, and even in the game's opening. These can be found in Skyward Sword, on the time gate, as it is about to be unlocked, and the trial gates. The trial gates also have a pattern that could be a lotus, feathers, or even scales. (Pictures to also follow) The time gate also has another connection. I have long proposed that the Temples of Time we have seen untill now have been connected by portals, even construction through higher dimensions. The cogs on either side of the gate of time emerge from portals. Portals, though a different color, are entered through the light temples, in Tears of the Kingdom. The temples also have a shape similar to the one that seals Zelda, in Skyward Sword.
Then we have the robotic people, and even guards. Their presence in both games generally use what looks like stone, and they all have floating body parts. Even Koloktos, from Skyward Sword.
I also thought the animal represented in the fire dungeons, in Skyward Sword were interesting. There are snakes and lions, which don't correlate to anything I can recall from Breath of the Wild, or Tears of the Kingdom. The frog may be related to the salamander that the salamander that Vah Rudania was based on, from Breath of the Wild, based on it being amphibians that connected to fire. Then there is the elephant relating to Vah Ruta. Then there are obviously birds... Vah Medoh.
As an aside, in the Skipper's Cabin, in Skyward sword, there is what looks like a biplane whale, which reminds me of the figure suspended from the ceiling of Purah's Lab, in Hateno. Many have suggested that this is a divine beast we have yet to see in action. (More pictures to follow.)
The final kicker, is the statue of the owl king!
Firstly, I would like to start with this image:
These designs are found around the goddess statue, in the sealed grounds, and a few other places, throughout Skyward Sword. These patterns are also found in the recent games, Breath of the Wild and Tears of the Kingdom, on many structures throughout Hyrule, such as the Lanayru Promenade. It would be easy for Hyrulian builders to replicate these features, and maintain them. To be clear, this does not suggest that the current structures, such as the promenade, were built by Zonai, as well. It does suggest that the society built after Skyward Sword has survived until Tears of the Kingdom. The sealed grounds, and the fallen Goddess statue would have been easily accessed by early Hyrulian builders. This means that there was only one Hyrule between the two games.
This continuation is further supported by the circuitry designs found on ancient Shiekah productions, found mostly in Breath of the Wild, but can also be found in Tears of the Kingdom. The designs are also seen in Skyward Sword. One example, I will present here:
But, the design is also seen on the portals of time, one of the boss keys, and on the sealing spike, all in Skyward Sword. There is at least one Shiekah in the past of Skyward Sword, so there is room for debate if all of this tech was created by Shiekah, from the beginning, or if this is one aspect they latched onto while reverse engineering Zonai technology. This gets even muddier when taking in the theory of time traveling Shiekah, originating from the future. Either way, this also indicates a continuum between the games.
Another connection, but even more vague, is the ship from Skyward Sword:
This ship has the ability to go invisible, which does not, as I am aware, carry over, but the color scheme, and patterns should look familiar, if you work through the main story of Tears of the Kingdom. Interestingly, the intended crew for this ship, in the picture, are robotic lifeforms, so it makes since that there is no galley.
In the ship, there is also an interesting symbol, on the walls:
Many have already suggested this to be a Zonai swirl, but the exact mark, minus the V shaped wings on either side, can be found on the bird (possibly Rito) like statues in the Thyphlo Ruins. I've always associated these swirls with the Kokiri, to be honest, but the connection to the Rito is interesting.
With the general connections, indicating a casual continuation, lets move onto the Zonai ruins we saw in Breath of the Wild. A major theme in these ruins were the dragon shapes. Huge square blocks were shaped to look like the Asian style dragon, and some carvings look like dragons moving back and forth, in a square shaped pattern. This carving can easily be found in the Thyphlo ruins, on some pillars, in Tears of the Kingdom. Then there are also some structures, in the depths, that have similar square shaped Asian style dragons, such as what are commonly called elevators. That easily connects with this key, from Skyward sword:
This Door:
And, this gate:
The gate style looks familiar. Here is another, from the same area, that is freestanding:
Many Zonai structures we find in Tears of the Kingdom have a similar basic building structure; namely the two pillars, topped with a header that runs past the two pillars. Many can be found freestanding, and not all with the same dealing. An example of this, in Tears of the Kingdom, is below the Death Mountain area. It is also important to point out that not all Zonai structures are shown to have this type of archway doorways. At least one round topped door is seen in one of the memories.
The door, in that memory is not the focus of the scene, so details beyond square patterns, and a lotus pattern are not easy to see. Though lotus patterns are also a common theme. In Tears of the Kingdom, they can be found in many places. I don't think the Zonai lights are meant to be lotus flowers, but bright blooms. The pasterns I am talking about can often be found in the little round device staging pads. Skyward Sword is full of Lotus shapes. Here are just a few:
This one being similar to the door in the memory I had mentioned.
And, this skylight being almost the exact same pattern as the device staging pads.
There are many more examples, and I encourage you to go back, and check out the game for yourself, but I need to keep the ideas moving. (I have also apparently reached the maximum ten pictures, so I will post the rest in a reply, as soon as I post this.) See, similar to the flower petals are designs that could be feathers, or scales. They can be found in many Zonai structures, adorning the walls, such as in the shrines. The most interesting example I found, in Skyward Sword, is found on the back of the head of the figure in the Ancient Cistern. I also see the cistern as a possible, in universe, prototype for the light shrines, in that it connects to the depths, and appears to be purifying the water. I also think this temple may reference the Zora and Rito existing before Skyward Sword, and I plan on making a deeper dive into that, at a later date, as that topic is bound to contain far more spoilers. Long story short, I believe the Cistern predates the light shrines, and even led to their eventual construction. Just look at the space below:
Plus, many of the structures feature round elements, that protrude out from the structure, some of which are even intended to be jumped from:
There is also the artwork detailing the history, presented in the beginning of Tears of the Kingdom. This style is called relief. While we don't see the same exact thing for Skyward Sword's prologue, looking more like paint on stone, We do see reliefs, providing information. Many of these reliefs utilize hard angles, just like the ones in Tears of the Kingdom. the differences between them are indicative of different artists using the same techniques.
Next are the glowing letters, related to holy power. If you have completed a light shrine, you have seen these. They are also in memories, and even in the game's opening. These can be found in Skyward Sword, on the time gate, as it is about to be unlocked, and the trial gates. The trial gates also have a pattern that could be a lotus, feathers, or even scales. (Pictures to also follow) The time gate also has another connection. I have long proposed that the Temples of Time we have seen untill now have been connected by portals, even construction through higher dimensions. The cogs on either side of the gate of time emerge from portals. Portals, though a different color, are entered through the light temples, in Tears of the Kingdom. The temples also have a shape similar to the one that seals Zelda, in Skyward Sword.
Then we have the robotic people, and even guards. Their presence in both games generally use what looks like stone, and they all have floating body parts. Even Koloktos, from Skyward Sword.
I also thought the animal represented in the fire dungeons, in Skyward Sword were interesting. There are snakes and lions, which don't correlate to anything I can recall from Breath of the Wild, or Tears of the Kingdom. The frog may be related to the salamander that the salamander that Vah Rudania was based on, from Breath of the Wild, based on it being amphibians that connected to fire. Then there is the elephant relating to Vah Ruta. Then there are obviously birds... Vah Medoh.
As an aside, in the Skipper's Cabin, in Skyward sword, there is what looks like a biplane whale, which reminds me of the figure suspended from the ceiling of Purah's Lab, in Hateno. Many have suggested that this is a divine beast we have yet to see in action. (More pictures to follow.)
The final kicker, is the statue of the owl king!