[Qt 6] re-enable tests for Qt 5 builds

Tests are disabled at the source level in MR !591 (merged) (and for some reason I missed it completely...). We should make sure we re-enable this as soon as possible, at least for Qt 5 and optionally for Qt 6 (see #605 (closed)). While we're at it, we probably should make it a build-time config flag.