LOTR: by what sorts of processes did Sauron reconstitute himself and his power after losing the Ring?

Just wondering if the OP was at all prompted by S2 Epi1 of The Rings of Power? Because there is a scene where Sauron reconstitutes himself from incorporeal form there and it was not at all what one would expect. Not like anything in anything I’ve ever read from Tolkien, but then nothing else in that show is either.