I would also like to know if there is a better way e.g. to check that references and links work. The only method I know of is to “view” the markdown files on Github.
The most reliable way is to build the documentation yourself locally:
using Pkg
Pkg.activate("docs")
include("docs/make.jl")
and then open the docs/build/index.html file in your favorite browser.
If it’s a repo you have access to, you can also activate PR docs preview with the push_preview argument to Documenter.deploydocs. But it will only work for repo insiders, not for PRs that come from a fork
If you click on the documenter/deploy commit status it takes you to the preview.
In your case it looks like Documenter managed to push the files, but it didn’t trigger GitHubs build and deploy. Most likely you haven’t set up the SSH deploy key correctly.