Add QA test for authorized push to protected branch

What does this MR do?

Adds a QA test for allowing authorized pushes to protected branches.

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

Why was this MR needed?

gitlab-com/migration#330 (comment 71275662)

Screenshots (if relevant)

Does this MR meet the acceptance criteria?

• Tests added for this feature/bug
• Review
  • Has been reviewed by Backend
• Conform by the style guides
• Squashed related commits together
• End-to-end tests pass (package-and-qa manual pipeline job)

What are the relevant issue numbers?