Tree-analyze test is successful for Framework and Engine changes; but we need to extract the specific "wait for engine" if we want to reuse this.

1. Create the composite action: .github/actions/wait-for-engine-build/action.yml
2. Move Check Engine Change + Wait for test check-in + Redirect engine.version to this file.
3. Update tree-analyze:

# ...
          - name: Wait for Engine Build
            uses: ./.github/actions/wait-for-engine-build
            with:
              github-token: ${{ secrets.GITHUB_TOKEN }}

          - uses: ./.github/actions/composite-flutter-setup
# ...

Now the GITHUB_ENV is updated correctly.