I did pkgdown::build_site() and usethis:::use_github_action(url = "https://raw.githubusercontent.com/r-lib/actions/master/examples/pkgdown.yaml") to set up gh-pages for the pkgdown site and it seems the site deploys only to get 404 on the github.io page.
I spend some time looking at github forums to finally realize that I miss a token on the repository. I don't know if I missed any steps, but I feel like a notification from pkgdown 'don't forget the token if you are to deploy to github' would be nice.
I have the same issue as @novica, I have checked the github action log but I could not find out what was the specific problem from it. I also checked the bookdown, the actions github page, the pkgdown site that you mentioned and lots of issues.