Update publish-docs.yml

Add permissions.
Correct formatting.

.github/workflows/publish-docs.yml

@@ -1,13 +1,17 @@
 name: Publish Docs
 
 on:
-  workflow_dispatch: { }
+  workflow_dispatch: {}
   workflow_run:
-    workflows: [ "Release (Production)" ]
+    workflows: ["Release (Production)"]
-    branches: [ main ]
+    branches: [main]
     types:
       - completed
 
+permissions:
+  contents: write
+  actions: read
+
 jobs:
   publish-docs:
     name: Publish Docs
@@ -26,8 +30,8 @@ jobs:
       - name: Setup python
         uses: actions/setup-python@v5
         with:
-          python-version: '3.10'
+          python-version: "3.10"
-          cache: 'pip'
+          cache: "pip"
           cache-dependency-path: |
             docs-requirements.txt
       - name: Install mkdocs