Add GH action to push hydrogen theme to external repo

.github/workflows/push-to-external-repo.yml

@@ -0,0 +1,36 @@
+name: (main) push to external repo
+
+env:
+  TEMPLATE_PATH: "templates/hydrogen-theme/**"
+
+on:
+  push:
+    branches:
+      - main
+    paths:
+      - ${{ env.TEMPLATE_PATH }}
+  pull_request:
+    branches:
+      - main
+    paths:
+      - ${{ env.TEMPLATE_PATH }}
+
+jobs:
+  push-to-external-repo:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout repository
+        uses: actions/checkout@v3
+
+      - name: Determine branch
+        id: branch
+        run: echo "::set-output name=branch::${{ github.event_name == 'pull_request' && github.event.action == 'opened' ? github.base_ref : github.ref }}"
+
+      - name: Publish to external repository
+        uses: peaceiris/actions-gh-pages@v3
+        with:
+          deploy_key: ${{ secrets.SSH_DEPLOY_KEY }}
+          publish_dir: ./templates/hydrogen-theme
+          external_repository: ${{ vars.EXTERNAL_REPO }}
+          publish_branch: ${{ steps.branch.outputs.branch }}
+          allow_empty_commit: true