Odd...
I do know that there are some accension points in the depths that can get you back to the surface. You can also chase down the dragons for a ride back up. So I dont think you are stuck there.
But I don't know why you wouldn't be able to teleport out.
If you've managed to get down from Sky Island without doing 4 shrines, that's 100% a bug, and if you can't teleport back up, I don't have a clue how to fix that.
I think you're stuck having to restart. Which sucks because Great Sky Island is notoriously the sloggiest part of the game. Not sure why it play so much worse than the Great Plateau.
Not a bug. The OP explains in the other post that they edited their heart count to open the Door of Time earlier than intended, which skips the cutscene that triggers the fourth shrine and the teleportation feature to be unlocked. You're not supposed to be able to teleport earlier than that, so the game works as intended (even tho it sucks for the OP to be stuck that way)
Not sure why it play so much worse than the Great Plateau.
100% agreed to that point tho. It takes AGES just to get to the shrines in the first place and locking the teleport feature up until the very end of the tutorial wasn't exactly the wisest design choice. In BotW the player can teleport as soon as there is a travel point unlocked, and story-wise it is weird that Link somehow forgot how fast travel works between the two games.