[CI] Run documentation-related tests

Summary

Eventually, we'll publish Operator documentation from the docs/ directory to docs.gitlab.com, similar to what we do with Charts. As a result, we should add documentation-related tests to our CI.

Acceptance criteria

• Documentation-related tests are added to the pipeline
  • markdownlint -> (!308 (merged))
  • Vale -> (!509 (merged))
  • check_docs_links (!462 (merged))
• For docs-only pipelines (docs-/-docs), only documentation-related tests run (!264 (merged))