GITHUB_TOKEN that is provided as a part of GitHub Actions doesn’t have authorization to create any successive events, such as GitHub Pages builds. So while you can push to the
gh-pages branch using the
GITHUB_TOKEN, it won’t spawn a GitHub Pages build. You’ll need to create a personal access token and supply it to your GitHub Action as a secret.
I used https://github.com/peaceiris/actions-gh-pages for a recent project because it already has a workaround for exactly this problem and seems to be actively maintained.
I hope that helps!