Pg does not cluster, so the only impact of a uuid is that you’re inserting in a random location location of the index, which is not great but not the end of the world (probably).

InnoDB clusters on the PK by default, so when you're inserting a UUID you're not only inserting in the middle of the index (on average) you're also inserting in the middle of the table.

And I don't know how much the on-disk storage has been optimised for this sort of things, but if the answer is "not" and sparse pages are not really a thing, you might need to rewrite half the table in order to do so.