Backport of "Extract EE specific files/lines for app/controllers/groups"

What does this MR do?

CE complement to https://gitlab.com/gitlab-org/gitlab-ee/merge_requests/5947

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

Why was this MR needed?

Screenshots (if relevant)

Does this MR meet the acceptance criteria?

• Changelog entry added, if necessary
• Documentation created/updated
• API support added
• Tests added for this feature/bug
• Conform by the code review guidelines
  • Has been reviewed by a UX Designer
  • Has been reviewed by a Frontend maintainer
  • Has been reviewed by a Backend maintainer
  • Has been reviewed by a Database specialist
• Conform by the merge request performance guides
• Conform by the style guides
• If you have multiple commits, please combine them into a few logically organized commits by squashing them
• Internationalization required/considered
• End-to-end tests pass (package-and-qa manual pipeline job)

What are the relevant issue numbers?

https://gitlab.com/gitlab-org/gitlab-ee/issues/5941