Merge and test genui integration

[polina-c]

Outline created based on discussion with @johnpryan:

• Enable basic golden testing, on presubmit, with local backend: Enable testWidgets to handle more complicated code. #3254
• Merge Improve UX of editing with AI (drafted by Brian). #3235
• Enable scheduled probes to make sure prod dartpad-genui works end-to end, using testWidgets
  • Make sure logging on backend is off for probes, if they run more often that daily: Turn off logging for testing calls. #3275
  • Implement the test
  • Make sure we recieve alerts for the failed tests
  • Enable tests on presubmit and hourly

[polina-c]

See drafted tests and discussion here: #3268