Change docs link check to markdown link checker

What does this MR do and why?

Change the docs link test to use the Lychee-powered CI/CD Markdown Link Check component.

• Before: https://gitlab.com/gitlab-org/gitlab/-/jobs/6272870564 (~6 minutes)
• After:
  • First run: https://gitlab.com/gitlab-org/gitlab/-/jobs/6230322901 (39 seconds, found 1 error not caught by old link check).
  • Second run: https://gitlab.com/gitlab-org/gitlab/-/jobs/6230337715 (40 seconds, now green due to link being fixed)

Related to technical-writing#995

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Before	After

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