Resolve "Milestone not updating in MR sidebar after selection"

What does this MR do?

Fixes a small bug in which changing the milestone while inside an MR causes the milestone to disappear (but it gets properly set and can be seen on a refresh).

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

I had to switch MergeRequestsController#update to using the MergeRequestWidgetSerializer. It shouldn't matter that there are extra attributes available now but just in case it would be good to validate.

Does this MR meet the acceptance criteria?

• Changelog entry added, if necessary
  • No changelog required for regressions in same milestone
• Conform by the code review guidelines
  • Has been reviewed by a Frontend maintainer
  • Has been reviewed by a Backend maintainer
• Conform by the merge request performance guides
• Conform by the style guides
• If you have multiple commits, please combine them into a few logically organized commits by squashing them

What are the relevant issue numbers?

Closes #47933 (closed)