I tried the example as defined here and it seems not to work out of the box. From my tests (I'm no expert with GitHub Actions and GitHub Pages at all) it seems that there is an issue with the permissions.
From what I understood so far, probably the following needs to be added to the Deploy Site - GitHub Action script on the bottom of the page:
permissions:
contents: write
pages: write
Additionally as stated in this discussion it looks like the deployment via the pipeline does no longer work with the instructions from the Guide.
I would be willing to update the Guide as soon as it is clarified what exactly the problem is.