[ci] Add commit steps to new runtime_commit_artifacts_v2

Adds back the missing steps with a few tweaks to where previously some
`github` context value was referenced, I changed it to read from the
triggering workflow_run (ie the build on `main`) instead.

ghstack-source-id: 4b0fa135f059ba925647b12972fa67ae2a49f2db
Pull Request resolved: https://github.com/facebook/react/pull/30476