Add group::not_owned to testcases; Add pre-hygiene

Dry-run: https://gitlab.com/gitlab-org/quality/triage-ops/-/jobs/340676064

Add group::not_owned to testcases; Add pre-hygiene

Introduce pre-hygiene so it runs before hygiene

We need to add the default group label before inference at the group level, so we need to make sure they run together and before that.

Closes #345 (closed)