The docs workflow actually does seem to rely on credentials for push.

Author: Julian

.github/workflows/docs.yml

@@ -12,7 +12,7 @@ jobs:
     steps:
       - uses: actions/checkout@v4
         with:
-          persist-credentials: false
+          persist-credentials: true
 
       - uses: extractions/setup-just@v2
       - name: Install Neovim