Improve the new driver test suite

[JanJakes]

The test suite for the new SQLite driver originates from the old driver tests being duplicated. As the test suite was growing over time, it would make sense to better categorize the tests, and check them against a real MySQL instance to make sure our assertions are correct. In doing so, we may consider always running them against both the SQLite driver and a MySQL container, and removing the hardcoded assertions.