Add a test step to the build docs CI

[PEZ]

The docs are built on pushes to the published branch. So it happens when we merge a PR directed at published, (which is where we instruct contributors to direct docs-only PRs).

However, it would be good if we could test that the docs build, and extra good if we published them somewhere so that contributors and reviewers can check the results easily.

[bpringe]

which is where we instruct contributors to direct docs-only PRs

Just a side note, we should put this instruction in the PR template.