Enable Hugo build test job for docs pipelines

What does this MR do?

Enables the Docs website test job we added in !4118 (merged).

This runs on docs pipelines. It will fail if it detects problems with docs content that will impact the website build.

The new website launches Feb 16-17, but we can enable this job now because GitLab Chart docs have been prepped to work with Hugo (via !4101 (merged)).

Successful pipeline run: https://gitlab.com/gitlab-org/charts/gitlab/-/jobs/9118357182

Related issues

gitlab-org/technical-writing/docs-gitlab-com#44 (closed)

Author checklist

For general guidance, please follow our Contributing guide.

Required

For anything in this list which will not be completed, please provide a reason in the MR discussion.

• Merge Request Title and Description are up to date, accurate, and descriptive.
• MR targeting the appropriate branch.
• MR has a green pipeline.
• Documentation created/updated.
• Tests added/updated, and test plan for scenarios not covered by automated tests.
• Equivalent MR/issue for omnibus-gitlab opened.

Reviewers checklist

• MR has a green pipeline on https://gitlab.com/gitlab-org/charts/gitlab.
• Consider downstream impact to the Operator, as per evaluating impact from changes to GitLab Chart.