It's kind of hard to keep track of tbh; The game tends to give contradictory information, or retcons things.
Originally in like...2.x it was the lifestream situation (Die -> Break down -> new soul). We're talking Minfillia days...but I think Endwalker had it that all souls technically don't break down, but instead have no memories and entirely different/new Aether.
The lore gets weird, and I don't think it's ever clear whether memory is tied to the soul, aether or something else (Dynamis?!)
I think it's currently something like:
A) Ascian aether/memory doesn't necessarily dissipate upon body-death, and they can possess/remake a body.
B) Unless the soul is trapped and flooded it with aether (a la white auracite)
C) ...except that even then the soul lingers/can be recalled (Emet helps out; Fandaniel in Aitiascope)
D) Future unsundered do not necessarily remember all their Ascian-self without the memory crystals (Amon/Gaia), but they might have some bits
Even then, I wouldn't say any of it is conclusive as the game tends to pull the carpet out from under us at this point (Hello Dynamis...).
As you said with Endwalker- we're at a point where different writers are changing established lore/concepts to fit their story, so I wouldn't be surprised if concepts are just thrown out the window/retconned.
