The way setting up GH pages publishing is described on https://github.com/ansible-community/github-docs-build/wiki/Getting-started-with-GitHub-Pages#enabling-pages is outdated and will stop working on June 30th, according to https://www.josephguadagno.net/2024/04/03/migrate-to-github-actions-from-pages-legacy-worker. Despite the mention of Jekyll all over that blog post this also affects publishing raw HTML pages (as used by the shared workflows from this repo).
Fixing this is probably quite easy, you simply need to add a workflow to the main branch that handles pushes to the gh-pages branch and publishes them (look for Static HTML Workflow Template in the blog post). I'll try this out later or tomorrow and will report back here how it went.
Ref: ansible-community/ansible-build-data#416