I believe everyone has the right of it: the timeline is bunk, this is a fairytale or myth, it is not concerned with continuity in any way. Hercules died of poison last week, but he is back and completing labors this week. Keep the party rocking.
THAT SAID
If you are trying to wedge this into a timeline somewhere:
The presence of the Rito at the founding of Hyrule screws everything up. The Rito are confirmed to be descendants of the Zora in Wind Waker. This does not preclude the existence of "divergent" Zora, but Wind Waker has a scene where a Rito is gesturing to a ghost Zora, and is basically like "That's my grandma." Given this evolution happened after the flooding of Hyrule, Zora and Rito should not be in the same room before Hyrule gets flushed down the toilet, left alone at the founding. So, with this in mind, the "far past" of Tears of the Kingdom must exist after the founding of New Hyrule in Spirit Tracks. To my knowledge, merged timelines or no, the Rito do not exist in any non-flooded timelines, and very much do not exist at earlier epochs.
BUT! The kicker here is the Master Sword. There is a stable time loop that involves Ganondorf awakening in the present, recognizing Link as the man he heard would kill him, Zelda being sent back in time, and Zelda telling everyone Ganondorf will be defeated by Link in the future-present. So there is technically a "this already happened thing" going on before the game starts. But the Master Sword is absent from the founding of Hyrule. We've got our God Cat-Goat People, and we've got our heroes from the various tribes, but nobody wields the Master Sword. Head Goat-Cat even seems to acknowledge "Future" Link as the hero because he is assured he has a magic sword. Ganondorf sees the Sword of Evil's Bane for the first time when he groggily first encounters Link. And, while the Master Sword gets her own time loop to heal, we do not know where or when the "pre-Botw" Master Sword is forged/found in this timeline. After all, with Ganondorf sealed away and only occasionally leaking out for events like the Calamity, the Master Sword was distinctly not forged to directly address Ganondorf as Tears of the Kingdom presents him.
So if we want to tie it all together, you could claim that the Master Sword has its singular origin in Skyward Sword, and its "end" was being driven into OoT "I hate sand" Ganondorf at the finale of Wind Waker. Then, at some waaaaay the heck later event, someone fished the Master Sword out of a "statue" well after OG Ganondorf leaked out and reincarnated into Ganondorf TotK. Or maybe the sea rescinded? Whatever the case, it had to happen after the founding of Nu-Hyrule, as the Master Sword missed Ganondorf's original TotK arrival. And the Master Sword just kind of "surfacing" after the sinking of Old Hyrule would also be consistent with the fact that the Triforce in both Breath of the Wild and Tears of the Kingdom seems to only exist in a spiritual manner, not in a physical "touch this and wish for your own dark world" fashion. Our favorite triangle is still kinda sealed, just the sword wiggled free.
One way or another, it all leads up to a TotK "Hyrule Founding" that had to happen after a previous Hyrule got wrecked. Assuming we do not ever get an alternate origin for the Master Sword, the (or a) "previous" Hyrule must have been the one that started with Skyward Sword.
And we've got a R2-D2 situation where Fi remembers everything.
These are my beliefs. At least for now.
Oh, and I still 100% believe the mundane explanation that Sheikah tech was manually bulldozed immediately after the completion of Breath of the Wild. I think the Zora (with their long lifespans) are the only people living in Hyrule that remember anything before being terrorized by laser death machines their entire lives. The minute "Sheikah Tech" wasn't fighting back, I am pretty sure people were disassembling it all with gusto.