Refactor dispatcher project branches path (EE)

What does this MR do?

EE Version of https://gitlab.com/gitlab-org/gitlab-ce/merge_requests/16398

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
• 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
• 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

What are the relevant issue numbers?

https://gitlab.com/gitlab-org/gitlab-ce/issues/41341