Experiment with a files-changed.json per PR (#161788)

This is an experiment to determine what the wall time of a (minimal)
"upload a JSON file describing files changed".

We are looking for this to take (low) single digit minutes, because if
we use this file (and expand it to become a build plan), it will block
almost _all_ other actions, and will likely get longer as we add more
complex logic and checks. Here's hoping!

.github/workflows/files-changed.yml

@@ -0,0 +1,37 @@
+name: Generate Changed Files JSON
+
+on:
+  pull_request:
+    types:
+      - opened
+      - synchronize
+
+jobs:
+  generate-json:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout code
+        uses: actions/checkout@v3
+
+      - name: Fetch base commit and origin/master
+        # Fetch what to compare the commit against
+        run: |
+          git fetch --no-tags --prune --depth=1 origin ${{ github.event.pull_request.base.sha }}
+          git fetch --no-tags --prune --depth=1 origin master
+          echo "FLUTTER_ENGINE_VERSION=${{ github.event.pull_request.base.sha }}" >> "$GITHUB_ENV"
+
+      - name: Initialize Dart SDK
+        # This downloads the version of the Dart SDK for the current platform.
+        run: |
+          ./bin/dart --version
+          cd dev/tools && ../../bin/dart pub get
+
+      - name: Write changed files to a JSON file
+        run: |
+          ./bin/dart run dev/tools/bin/get_files_changed.dart --since="${{ github.event.pull_request.base.sha }}" > changed_files.json
+
+      - name: Upload artifact
+        uses: actions/upload-artifact@v4
+        with:
+          name: changed-files
+          path: changed_files.json