* not the same as your internal DB row primary keys, which in Postgres should usually be bigserial
Yes, in that there are DB technologies not built in a fashion where records are stored in a sorted order of some fashion. No, in that they are very much not common technologies. Most databases, relational, non-relational, etc have some form of a B-Tree at their core somewhere.
MySQL docs claim that a hash index is much faster if you only need kv lookups, so it seems like uuid4 with hash index would be suitable. Never tried it though, and can't say whether it's faster than using a btree with uuid7. Seems like in theory it would be.
Hash maps should generally always have faster lookups than Btree based structures. However, they'll have slower writes especially when contested. A key issue hash tables have to deal with is what happens when a remapping needs to happen. For example, when 2 keys have the same hash. In that case, locking becomes a lot more messy.
For a btree this is simpler. It's built to be able to handle reshuffling and rebalancing in a way that's semi easy to have fine grained locks around.