Expand Playwright test coverage for XB AI module

Over in 📌 Add Playwright tests for XB AI module Active (in MR 1466) the test "Should verify AI panel API request and response payload" was removed in an effort to reduce flakiness.

I'm dropping this comment here to acknowledge that it probably needs to be reinstated as part of this ticket in some form. However @justafish mentioned in chat that "I've commented out the API endpoint test as I don't think this is the appropriate place to test the structure of an API response" so perhaps a different approach would make sense.