Move postsubmit testing to main.

[godofredoc]

Moving post-submit testing to main is required for unblock the roll of
depot_tools.

Bug: flutter/flutter#90476

Pre-launch Checklist

• I read the Contributor Guide and followed the process outlined there for submitting PRs.
• I read the Tree Hygiene wiki page, which explains my responsibilities.
• I read and followed the Flutter Style Guide and the C++, Objective-C, Java style guides.
• I listed at least one issue that this PR fixes in the description above.
• I added new tests to check the change I am making or feature I am adding, or Hixie said the PR is test-exempt. See testing the engine for instructions on
  writing and running engine tests.
• I updated/added relevant documentation (doc comments with ///).
• I signed the CLA.
• All existing and new tests are passing.

If you need help, consider asking for advice on the #hackers-new channel on Discord.

[CaseyHillers]

This would need to be landed on main.