Add Storybook GitHub workflow for publishing to GH pages (#51235)

* Add storybook workflow

* Update version and add trigger for push on trunk

* Add workflow_dispatch for manual trigger also

* Add permissions

* Add trigger for current branch

* Set install to true for monorepo setup

* Add write permissions

* Use hashes for GH action versions and add --quiet for building storybook

* Remove on push trigger for now

.github/workflows/storybook-pages.yml

@@ -0,0 +1,34 @@
+name: Storybook GitHub Pages
+
+on:
+    workflow_dispatch:
+
+permissions:
+    contents: write
+
+jobs:
+    deploy:
+        runs-on: ubuntu-latest
+        if: ${{ github.repository == 'woocommerce/woocommerce' }}
+
+        steps:
+            - name: Checkout
+              uses: actions/checkout@692973e3d937129bcbf40652eb9f2f61becf3332 # v4.1.7
+              with:
+                  ref: trunk
+                  fetch-depth: 0
+
+            - name: Setup WooCommerce Monorepo
+              uses: ./.github/actions/setup-woocommerce-monorepo
+              with:
+                  install: true
+
+            - name: Build Storybook
+              run: pnpm --filter='@woocommerce/storybook' build-storybook --quiet
+
+            - name: Deploy
+              uses: peaceiris/actions-gh-pages@4f9cc6602d3f66b9c108549d475ec49e8ef4d45e # v4.0.0
+              with:
+                  github_token: ${{ secrets.GITHUB_TOKEN }}
+                  publish_dir: ./tools/storybook/storybook-static
+                  force_orphan: true