Are there any clear downsides to sequential prefixes on UUIDs? I would imagine if you're producing new objects at a high enough rate, you'd have a lot of prefix collisions, which would hinder search times. I've never benchmarked to confirm that though.
If the prefix is incremented for every new ID, you essentially have the same problem as you do with serial: you leak information about the amount of rows in some timeframe.
As the link posted above mentions, you can alternatively use a timestamp-based prefix that wraps around after all the bits have been used. This one still leaks possible creation times of the record, so it's on par or better compared to UUIdv6, ULID, etc. (because here the exact creation time can't necessarily be deduced).
In all of these UUID solutions apart from the fully random v4, you are trading of the better index performance with some level of information leakage about the record the ID is associated with.