[CQ] API: migrate from to-be-removed AnActionListener APIs

[pq]

Migrate to safe AnActionListener APIs.

This migration has been attempted before but was reverted as possibly causing a hot reload regression (#6996).

I've confirmed that hot reload works (Mac OS Meerkat) but have preserved the note in case anything odd happens.

See: #7718

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 the Flutter Style Guide recently, and have followed its advice.
• I signed the CLA.
• I listed at least one issue that this PR fixes in the description above.
• I updated/added relevant documentation (doc comments with ///).
• I added new tests to check the change I am making, or this PR is test-exempt.
• All existing and new tests are passing.

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

[jwren]

Giving approval, but do land this with caution. Do build it and try the zip to validate that we don't do a push which breaks it.

Also, 🎉