Resolve "Can't close issue through buttons in the textarea on mobile"

What does this MR do?

When the user clicked on the closr/reopen issue button from within the Vue app it was triggering a click outside of the Vue app. The old code was looking for a visible button that on mobile was never visible.

This MR removes the outside click trigger and makes the request from withing the Vue app keeping the behavior of updating the top header section.

It also improves UX by not renaming the button from "close issue" to "reopen issue" before the request is made.

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
• End-to-end tests pass (package-qa manual pipeline job)

What are the relevant issue numbers?

Closes #42923 (closed)