Is your feature request related to a problem or challenge? Please describe what you are trying to do.

There have been a few cases where we have added documentation to either the docstrings or the rst files that have generated errors when running our generator. CI should catch these.

Describe the solution you'd like

Add a CI check that fails when documentation generates any error.

Describe alternatives you've considered

None

Additional context

For example, #1132 and #1040 both resulted in generator problems but CI passed for both of them.