Add publish-docs job to release workflow

.github/workflows/release.yml

@@ -35,10 +35,35 @@ jobs:
       - name: Push Python artifacts to PyPI
         uses: pypa/[email protected]
 
-  publish-github:
+  publish-docs:
     needs: publish-pypi
     runs-on: ubuntu-latest
 
+    steps:
+      - uses: actions/checkout@v3
+        with:
+          fetch-depth: 0
+          submodules: true
+
+      - name: Setup Python
+        uses: actions/setup-python@v4
+        with:
+          python-version: 3.8
+
+      - name: Install Hatch
+        run: pip install --upgrade hatch
+
+      - name: Get version from tag
+        id: get-version
+        uses: battila7/get-version-action@v2
+
+      - name: Deploy documentation
+        run: hatch run docs:deploy ${{ steps.get-version.outputs.version-without-v }}
+
+  publish-github:
+    needs: publish-docs
+    runs-on: ubuntu-latest
+
     permissions:
       id-token: write