Reland unit test UI against local backend.

[polina-c]

1. Reverts Revert "Unit test against local backend." #3280 to reland Unit test against local backend. #3278, that failed with Compilation fails due to CORS error #3279
2. Test covers populateVersions that maybe caused the issue.
3. Removes probes from UI testing, as we plan to create them differently in pkgs/dartpad_services

Fixes #3284

[github-actions]

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