One explanation is that ol’ Palps levitated himself onto a walkway down the elevator shaft after shooting blue ribbons out of his hands and then hopped onto a shuttle.
Another possibility is that his body landed on a catwalk and a Praetorian guard found it and got it out on a shuttle for future reanimation.
Or if you wanted to get really crazy and use clones, the Palpatine on DS2 could have been the clone, explaining his clear insanity.
The absolute worst way to go would have the original body die and bring him back as a clone.
The problem with the “he just landed” answer is basically…it’s mundane. The climax of the the entire trilogy is negated by him escaping like Grevious “time to abandon ship hee hee hee.”
Three words: Ming always escapes.
It also, from a narrative sense, ruin Luke’s confrontation since Palp was never in danger since he can just walk away even from falling 1000000 feet.
On the contrary, it clarifies that Luke’s only intention was to save his father. He believed that if he were taken to the Emperor they would all die in the Alliance attack. Palpatine dying from either his hand or his fathers was never stated by Luke as his goal.
Thematically, it ruins the whole trilogy, since Anakin’s sacrifice is instantly negated. Sort of like how JJ kept undoing Chewie and 3po and Ben Solo’s deaths 30 seconds later. At least with a clone, it thematically fits in the sense of “he came back…but wrong, undoing death has consequences.”
Anakin’s sacrifice is also clarified - His intention becomes unequivocally one of saving his son rather than doing another murder.