Use lychee to check for broken links

What does this merge request do and why?

As part of evaluating lychee for checking for broken links (gitlab!143171 (closed)), try it out in the GDK project where we've never compiled to HTML.

• technical-writing#979

Impacted categories

The following categories relate to this merge request:

• gdk-reliability - e.g. When a GDK action fails to complete.
• gdk-usability - e.g. Improvements or suggestions around how the GDK functions.
• gdk-performance - e.g. When a GDK action is slow or times out.

Merge request checklist

• This change is backward compatible. If not, please include steps to communicate to our users.
• Tests added for new functionality. If not, please raise an issue to follow-up.
• Documentation added/updated, if needed.
• Announcement added, if change is notable.
• gdk doctor test added, if needed.
• Add the ~highlight label if this MR should be included in the CHANGELOG.md.