Decouple more of Repository from Rugged

What does this MR do?

This MR chips away at decoupling the Repository class from Rugged.

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

These changes touch caching sensitive code.

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
• 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-qa manual pipeline job)

What are the relevant issue numbers?

Closes gitaly#969 (closed)