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.” 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.
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.”
With a clone, especially as it’s degrading from “Dark Side” alchemy, it also explains why the Star Wars universe DOES NOT use clone tech to resurrect people.