SQL: resolve legacy mode + deprecate mysql flavor (GH6900)

- removed warning for not using sqlalchemy (as sqlite DBAPI connection is fully supported, no warning needed)
- added deprecation warning for 'mysql' flavor
- removed necessity of providing flavor kwarg (no warning if not provided, assumed to be sqlite3)
- removed `flavor` kwarg from execute and read_sql_query (because a) are not database specific functions + b) would only be needed for mysql, but this will is deprecated so no need to introduce it)
- updated the tests to reflect this
- updated docs and docstrings to reflect that sqlite3 is the only but fully supported DBAPI connection (no 'legacy')

Closes #6900.