Refactor Github Action per b/485167538

[google-admin]

This is a http://go/LSC run by http://go/ghss to automatically refactor your Github Actions per http://b/485167538.

This is a PR to help you upgrade to the latest standards in Github Actions.

Please merge this PR to accept the changes. NOTE: if you do not accept this PR, it may be force merged by the GHSS team. See http://b/485167538 for more details.

[gemini-code-assist]

Note

Gemini is unable to generate a summary for this pull request due to the file types involved not being currently supported.

[paulb777]

LGTM on good CI

[paulb777]

Perhaps out of scope for this PR, but iOS has found it useful to trigger workflows on changes to workflow itself like https://github.com/firebase/firebase-ios-sdk/blob/main/.github/workflows/sdk.auth.yml#L12

[a-maurice]

Perhaps out of scope for this PR, but iOS has found it useful to trigger workflows on changes to workflow itself like https://github.com/firebase/firebase-ios-sdk/blob/main/.github/workflows/sdk.auth.yml#L12

Yeah, we have that setup on C++. Unity has a problem with limited licenses though, so it is set up to require manual work. You can either add a label, but I tend to just manually kick it off (see https://github.com/firebase/firebase-unity-sdk/actions/runs/22203613060 for the most recent one), and when it all works, I add a link back to the commit to the working one.

[a-maurice]

Integration tests mostly pass, beyond some flakes