Is this a new feature, an improvement, or a change to existing functionality?

New Feature

How would you describe the priority of this feature request

Critical (currently preventing usage)

Please provide a clear description of problem this feature solves

We currently check links for Markdown/RST files included in the documentation builds, however the example README.md files are not included in this.

Describe your ideal solution

Check links in CI

Additional context

No response

Code of Conduct

• I agree to follow this project's Code of Conduct
• I have searched the open feature requests and have found no duplicates for this feature request