Use `GITHUB_TOKEN` to deploy from public repositories once possible

[gomorizsolt]

Follow-up: https://github.community/t5/GitHub-Actions/Github-action-not-triggering-gh-pages-upon-push/m-p/31266/highlight/true#M743

Private repositories can use the GITHUB_TOKEN secret to deploy to GitHub Pages. In the case of public repositories, however, server-to-server requests do not kick off a page build because GITHUB_TOKEN does not have authorization to create any successive events. Therefore, opting for a different authorization method is a must in this case to spawn a page build. Our recommendation, and because it's how the deployment workflow is set up, is generating a deployment key for this specific use-case.