Loading spinner not stop even on errors in the Issuable Templates

What does this MR do?

Makes it better to handle errors on API requests in Issuable Templates by correctly stopping the loading spinner.

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

No.

Why was this MR needed?

To improve user experience when users have client-side errors.

Screenshots (if relevant)

n/a

Does this MR meet the acceptance criteria?

• Changelog entry added, if necessary
• [n/a] Documentation created/updated
• [n/a] API support added
• [n/a] Tests added for this feature/bug
• Review
  • Has been reviewed by UX
  • Has been reviewed by Frontend
  • [n/a] Has been reviewed by Backend
  • [n/a] Has been reviewed by Database
• Conform by the merge request performance guides
• Conform by the style guides
• Squashed related commits together
• [n/a] Internationalization required/considered

What are the relevant issue numbers?

Closes #40029 (closed)