Add a job to test doc building (for realsies this time)
# What does this PR do?

This PR takes over from #14645 to do it properly this time, meaning:
- we don't rely on secrets anymore which doesn't work for pull-request
- we don't need the secrets as we are not pushing anywhere
- we actually checkout the content after the PR merge, and not just master 🤦 

Just rebased on `master` and force-pushed.<|||||>Checking that it fails as it's missing the `kenlm` dependency, which I will add right after I confirm it fails.<|||||>Yes the object and its docstings exist whether or not `kenlm` is installed.