Port of 39880-merge-method-api to EE

What does this MR do?

It ports my changes from gitlab-ce!18031 (add merge_method to projects api) to gitlab-ee.

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

Honestly, I have no idea if that's anywhere near right. I just blindly followed the instructions in the build log and hope that's about right.

Why was this MR needed?

Because the changes in the above mentioned request could not be applied cleanly.

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 Backend
• Conform by the merge request performance guides
• Conform by the style guides
• Squashed related commits together

What are the relevant issue numbers?

gitlab-ce#39880

See also gitlab-ce!18031