Thanks @jimmiemunyi for alerting us to this, repeating my answer from another thread here incase someone finds this thread via a search:
It turns out we cannot enable GitHub pages for private repos through GitHub Actions automatically due to security constraints. You will have to enable GitHub pages yourself. I have edited the Actions workflow to provide more helpful error messages, where possible indicating that you have to enable this yourself. If you try to make a change in your docs you should see the new error messages come up.