Improve Web IDE Commit Panel

What does this MR do?

Improves the commit panel interaction flow making it more consistent, as per #44837 (closed).

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

⚠ This branch is based on an unmerged one: !17898 (merged)

We might merge this into that or wait for it to be merged to master. To be determined. /cc @iamphill

Why was this MR needed?

Lack of consistency, as described in the issue.

Screenshots (if relevant)

Does this MR meet the acceptance criteria?

• Changelog entry added, if necessary
• Documentation created/updated
• Tests added for this feature/bug
• Review
  • Has been reviewed by UX
  • Has been reviewed by Frontend
• Conform by the merge request performance guides
• Conform by the style guides
• Squashed related commits together

What are the relevant issue numbers?

Closes #44837 (closed)