Extract install-action-manifest-schema and publish to crates-io (#657)

Signed-off-by: Jiahao XU <Jiahao_XU@outlook.com>
Co-authored-by: Taiki Endo <te316e89@gmail.com>

.github/workflows/manifest_sync.yml

@@ -0,0 +1,51 @@
+name: Manifest Synchronization
+
+permissions:
+  contents: read
+
+on:
+  release:
+    types: [released]
+
+env:
+  WORKSPACE: /tmp/workspace
+
+defaults:
+  run:
+    shell: bash --noprofile --norc -CeEuxo pipefail {0}
+
+jobs:
+  sync:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+        with:
+          persist-credentials: true
+
+      - name: Checkout manifest-schema branch
+        run: ./tools/ci/checkout-manifest-schema-branch.sh "${WORKSPACE}"
+
+      - name: Copy over schema
+        run: cp -- ./manifests/* "${WORKSPACE}"
+
+      - name: Stage changes
+        working-directory: ${{ env.WORKSPACE }}
+        run: git add .
+
+      - name: Show diff
+        working-directory: ${{ env.WORKSPACE }}
+        run: git diff HEAD
+
+      - name: Detect changes
+        id: changes
+        working-directory: ${{ env.WORKSPACE }}
+        run: |
+          # This output boolean tells us if the dependencies have actually changed
+          printf "count=%s\n" "$(git status --porcelain=v1 | wc -l)" >>"${GITHUB_OUTPUT}"
+
+      - name: Commit and push
+        # Only push if changes exist
+        if: steps.changes.outputs.count > 0
+        working-directory: ${{ env.WORKSPACE }}
+        run: |
+          git commit -m "Update manifest schema" && git push origin HEAD