WIP: Add assign-to-me link

What does this MR do?

Adds the assign-to-me link.

This needs some refactor work. I'm going to find a way to do it quickly for the regression with a integration test, but will open an issue to refactor this whole component.

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

Why was this MR needed?

Screenshots (if relevant)

Does this MR meet the acceptance criteria?

• Changelog entry added
• Documentation created/updated
• API support added
• Tests
  • Added for this feature/bug
  • All builds are passing
• Conform by the merge request performance guides
• Conform by the style guides
• Branch has no merge conflicts with master (if it does - rebase it please)
• Squashed related commits together

What are the relevant issue numbers?

Closes #23948 (closed)