Test external links with Lychee

What does this MR do and why?

To contribute to: technical-writing#979, convert our external link tests to Lychee.

• Test job for gitlab: https://gitlab.com/gitlab-org/gitlab-docs/-/jobs/6984489443
• Test job for omnibus-gitlab: https://gitlab.com/gitlab-org/gitlab-docs/-/jobs/6984489444
• Test job for gitlab-runner: https://gitlab.com/gitlab-org/gitlab-docs/-/jobs/6984489445
• Test job for charts: https://gitlab.com/gitlab-org/gitlab-docs/-/jobs/6984489447
• Test job for gitlab-operator: https://gitlab.com/gitlab-org/gitlab-docs/-/jobs/6984489448

Merge request acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• I have evaluated the MR acceptance checklist for this merge request.