WIP: Fix `updated_at` doesn't apply to `state_event` updates of issues via API

What does this MR do?

This is another attempt at fixing #46980 (closed), reflecting the helpful comments by @smcgivern and @jprovaznik in !23713 (closed).

This is still a work-in-progress but I'm opening this as a placeholder for the time being. Preliminary reviews are always welcome.

What are the relevant issue numbers?

• Closes #46980 (closed)

Does this MR meet the acceptance criteria?

• Changelog entry added, if necessary
• Documentation created/updated
• Tests added for this feature/bug
• Tested in all supported browsers
• Conforms to the code review guidelines
• Conforms to the merge request performance guidelines
• Conforms to the style guides
• Conforms to the database guides
• Link to e2e tests MR added if this MR has Requires e2e tests label. See the Test Planning Process.
• Security reports checked/validated by reviewer