Try contents: write.

.github/workflows/mkdocs-publish.yml

@@ -11,10 +11,6 @@ on:
   # Allows you to run this workflow manually from the Actions tab
   workflow_dispatch:
 
-permissions:
-  contents: read
-  pages: write
-
 # A workflow run is made up of one or more jobs that can run sequentially or in parallel
 jobs:
   # This workflow contains a single job called "build"
@@ -37,5 +33,8 @@ jobs:
       - name: MkDocs build
         run: mkdocs build
 
+  deploy:
       - name: MkDocs deploy
         run: mkdocs gh-deploy --force
+        permissions:
+          contents: write