feat: integrate with unified docs repository (#10830)

Co-authored-by: openhands <openhands@all-hands.dev>

.github/workflows/dispatch-to-docs.yml

@@ -0,0 +1,23 @@
+name: Dispatch to docs repo
+
+on:
+  push:
+    branches: [main]
+    paths:
+      - 'docs/**'
+  workflow_dispatch:
+
+jobs:
+  dispatch:
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        repo: ["All-Hands-AI/docs"]
+    steps:
+      - name: Push to docs repo
+        uses: peter-evans/repository-dispatch@v3
+        with:
+          token: ${{ secrets.ALLHANDS_BOT_GITHUB_PAT }}
+          repository: ${{ matrix.repo }}
+          event-type: update
+          client-payload: '{"ref": "${{ github.ref }}", "sha": "${{ github.sha }}", "module": "openhands", "branch": "main"}'