If you were using something like UUIDv4, you wouldn't be exposing that information at all though, neither in cleartext or ciphertext. It seems weird to say, "the user ID contains secret information so we encrypt it with an eternal fixed pre-shared key then share the ciphertext with the world", when you could've just said "the user ID contains no secret information".

It feels like the right solution here is to pick between: use UUIDv7 and treat the account creation time as public information, or use an identifier scheme which doesn't contain the account creation time.

An incrementing version number would once again leak time information. Even a not incrementing version number would leak that kind of information, because if you know the timestamp of another ID with the same version.

I think there is no good alternative to random external identifiers.