Repository verification on Geo secondary

What does this MR do?

EE counterpart of gitlab-org/gitlab-ce!18484

It includes the refactors of that MR and uses those to make it possible to run the repo checks (i.e. git fsck) on the Geo secondary too.

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

• EE specific content should be in the top level /ee folder

• Conform by the merge request performance guides

• Conform by the style guides

• Squashed related commits together

• Internationalization required/considered

• If paid feature, have we considered GitLab.com plan and how it works for groups and is there a design for promoting it to users who aren't on the correct plan

• End-to-end tests pass (package-qa manual pipeline job)

What are the relevant issue numbers?

Closes gitlab-org/gitlab-ee#5564, gitlab-org/gitlab-ee#4746