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.
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.