Add Spotless check format workflow

.github/workflows/check_format.yml

@@ -0,0 +1,73 @@
+name: Check Format
+concurrency:
+  group: ${{ github.workflow }}-${{ github.event.pull_request.number || github.ref }}
+  cancel-in-progress: true
+on:
+  pull_request:
+  push:
+    branches:
+      - main
+
+jobs:
+  determine_changed:
+    name: "Determine changed modules"
+    runs-on: ubuntu-22.04
+    if: (github.repository == 'Firebase/firebase-android-sdk' && github.event_name == 'push') || github.event_name == 'pull_request'
+    outputs:
+      modules: ${{ steps.changed-modules.outputs.modules }}
+    steps:
+      - uses: actions/[email protected]
+        with:
+          fetch-depth: 2
+          submodules: true
+
+      - name: Set up JDK 17
+        uses: actions/[email protected]
+        with:
+          java-version: 17
+          distribution: temurin
+          cache: gradle
+
+      - id: changed-modules
+        run: |
+          git diff --name-only HEAD~1 | xargs printf -- '--changed-git-paths %s\n' | xargs ./gradlew writeChangedProjects --output-file-path=modules.json
+          echo modules=$(cat modules.json) >> $GITHUB_OUTPUT
+
+  check_format:
+    name: "Check Format"
+    runs-on: ubuntu-22.04
+    needs:
+      - determine_changed
+    strategy:
+      fail-fast: false
+      matrix:
+        module: ${{ fromJSON(needs.determine_changed.outputs.modules) }}
+
+    steps:
+      - uses: actions/[email protected]
+        with:
+          fetch-depth: 2
+          submodules: true
+
+      - name: Set up JDK 17
+        uses: actions/[email protected]
+        with:
+          java-version: 17
+          distribution: temurin
+          cache: gradle
+
+      - name: ${{ matrix.module }} Check Format
+        run: |
+          ./gradlew ${{matrix.module}}:spotlessCheck
+
+  # A job that fails if any job in the check_format matrix fails,
+  # to be used as a required check for merging.
+  check_all:
+    runs-on: ubuntu-22.04
+    if: always()
+    name: Check Format (matrix)
+    needs: check_format
+    steps:
+      - name: Check matrix
+        if: needs.check_format.result != 'success'
+        run: exit 1