The Shrine of Resurrection on the Great Plateau
Built by the Sheikah to bring people back to life (… or at least heal otherwise mortal wounds if the patient in question is not quite dead yet). The structure directly above the pool where Link awoke looks a bit like the lower part of a Guardian Stalker, and the entire device is supported by thick, glowing vines or tubes, adorned with the typical Jōmon pottery patterns found inside of shrines and on most “ancient tech”.
Ganon’s Cocoon inside the Sanctum
The cocoon inside the Sanctum is supported by the same kind of vines / tubes, only that they’re glowing red instead of blue. There is also the same kind of “lower Guardian Stalker piece” just barely visible right above the actual cocoon, and most of the device seems to be consumed by Malice. Since both the cocoon containing Ganon’s unfinished body and the little pool where Link awoke are directly below the “Guardian Butt” of the respective devices, it is safe to assume that the actual healing / resurrecting process takes place in precisely that spot.
As far as I know, those vines / tubes are one-of-a-kind and only appear inside the Shrine of Resurrection and the Sanctum. I can’t think of any other place in Hyrule with those (but please feel free to correct me if there are any).
Plus, the Creating a Champion artbook mentions that both devices were specifically designed with the same concept in mind:
^(page 223)^
As for why Zelda emerged from inside of the cocoon and what she had been doing for the past 100 years, there is also an answer in the same book: she was basically eaten by Ganon and gave him the worst stomach ache imaginable for a whole century to keep him occupied. No wonder that dude is so ill-tempered. Imagine having cramps for 100 years straight …
However, that alone wasn’t enough to defeat him. It was merely enough to stall the invasion for a century and keep Ganon confined to the cocoon, with a not-quite-yet-finished body that wasn’t actually ready to emerge the moment Link entered the Sanctum.
^(page 410)^
That last sentence also seems to imply that Zelda herself might be the reason Guardian Stalkers and Skywatchers stay in one place instead of wandering off, and the Divine Beasts aimlessly walk/fly in circles or sit in lakes instead of going elsewhere. It would have been super easy for, say, Vah Medoh to glide over to the Great Plateau and simply blast up the whole thing - but instead it just circles over Rito Village, basically doing nothing. They seem to be merely on autopilot because their supervisor is busy trying to get rid of the half-deity he swallowed, so he simply isn’t able to give them proper orders.