Resolve "API v4 allows setting a branch that doesn't exist as the default one"

What does this MR do?

This MR adds checks for branch existence before setting it as the default branch.

Why was this MR needed?

Current behavior allows to set a branch as the default branch even if this branch does not exist.
After that git checkout is broken because of unexisted ref.

Does this MR meet the acceptance criteria?

• Changelog entry added, if necessary
• Documentation created/updated
• API support added
• Tests
  • Added for this feature/bug
  • All builds are passing
• 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
• Branch has no merge conflicts with master (if it does - rebase it please)
• Squashed related commits together

What are the relevant issue numbers?

Closes #36010 (closed)