At that point—why bother with the mock at all? Cutting out the intermediary and running integration tests of your application against a real database will be faster.
You can’t use SQLite here either because all SQLite isolation levels are serializable anyway, which is _very_ different from how PostgreSQL works. Testing against SQLite could end up giving you a false sense of security that your code is safe against race conditions, whereas in reality it’s vulnerable when connected to a PostgreSQL server because of the difference in default isolation levels
At this level of testing detail the only real option is to test against a real database that matches what you’re running in production. Otherwise you’re just testing a mock.