I'm also not a huge fan of leaking server-side information; I suspect UUIDv7 could still be used in statistical analysis of the keyspace (in a similar fashion to the german tank problem for integer IDs). Also, leaking data about user activity times (from your other comment) is a *really* good point that I hadn't considered.
I've read people suggest using a UUIDv7 as the primary key and a UUIDv4 as a user-visible one as a remedy.
My first thought when reading the suggestion was, "well but you'll still need an index on the v4 IDs, so what does this actually get you?" But the answer is that it makes joins less expensive; you only require the index once, when constructing the query from the user-supplied data, and everything else operates with the better-for-performance v7 IDs.
To be clear, in a practical sense, this is a bit of a micro-optimization; as far as I understand it, this really only helps you by improving the data locality of temporally-related items. So, for example, if you had an "order items" table, containing rows of a bunch of items in an order, it would speed up retrieval times because you wouldn't need to do as many index traversals to access all of the items in a particular order. But on, say, a users table (where you're unlikely to be querying for two different users who happen to have been created at approximately the same time), it's not going to help you much. Of course the exact same critique is applicable to integer IDs in those situations.
Although, come to think of it, another advantage of a user-visible v4 with v7 Pk is that you could use a different index type on the v4 ID. Specifically, I would think that a hash index for the user-visible v4 might be a halfway-decent way to go.
I'm still not sure either way if I like the idea, but it's certainly not the craziest thing I've ever heard.
I think a bigger benefit from doing that would be that inserts would be cheaper. Instead of an expensive insert into the middle of an index for every table that needs an index on that key, you can do a cheaper insert at the end of the index for all of them except for the one that uses uuid4.
But if you are doing that, why not just use an incrementing integer instead of a uuidv7?