Add a CI job to test the docs website build

What does this MR do?

1. Adds a CI job to test that docs pages can build on Hugo. This test validates file structure and shortcode syntax for the new website.

   • Example job: https://gitlab.com/gitlab-org/gitlab-runner/-/jobs/9105886578

2. Updates references to the lint-markdown Docker image to reflect its new location.

   • docs: lint markdown: https://gitlab.com/gitlab-org/gitlab-runner/-/jobs/9094803285

Related issues

• Add Hugo build tests to docs content pipelines (gitlab-org/technical-writing/docs-gitlab-com#161 - closed) • Sarah German
• Very similar MR for gitlab-operator: gitlab-org/cloud-native/gitlab-operator!1065 (merged). This test is being added to every repo that publishes to docs.gitlab.com.

What's the best way to test this MR?

Review pipeline output.

What are the relevant issue numbers?