Various improvements to repository checks

What does this MR do?

Repository checks were built a long time ago, and they didn't receive much love in all these year. This MR cleans up bit (in preparation for gitlab-org/gitlab-ee#5564).

Are there points in the code the reviewer needs to double check?

Should we use Feature flipper instead of admin settings to disable/enable this setting?

Does this MR meet the acceptance criteria?

• Changelog entry added, if necessary
• Documentation created/updated
• API support added
• Tests added for this feature/bug
• Review
  • Has been reviewed by UX
  • Has been reviewed by Frontend
  • Has been reviewed by Backend
  • Has been reviewed by Database
• Conform by the merge request performance guides
• Conform by the style guides
• Squashed related commits together
• Internationalization required/considered
• End-to-end tests pass (package-and-qa manual pipeline job)

What are the relevant issue numbers?

gitlab-org/gitlab-ce#45046