Simplify markdown link check

I've suggested in `dotnet/core` usage of markdown link check but seems they found a better way to run this:

https://github.com/dotnet/core/pull/8346/files

We should consider doing it similarly (also follow up test PR if setup in fact does find errors).

And seems it's possibly to run this only on modified files which makes it even better because there will be less noise. We can consider still running checking all links as part of nightly though.

Also seems there might be easy way to set this up: https://github.com/gaurav-nelson/github-action-markdown-link-check