[FEATURE REQUEST] Use Github Action to check Markdown links

[kevinjqliu]

Is your feature request related to a problem? Please describe.

Use github-action-markdown-link-check Github Action to check for dead links in Markdown files.

Similar to iceberg-python#324

Describe the solution you'd like

No response

Describe alternatives you've considered

No response

Additional context

No response

[bbrewington]

I'm working on this on a fork, and will PR in

Just read CONTRIBUTING.md, and emailing over my ICLA now

[kevinjqliu]

I had a PR started, but feel free to work on this! Feel free to add me as a reviewer

Should cover both docs/ and regtests/client/python/docs

[kevinjqliu]

As a follow up, enable this github action for all MD files and for all PRs
See comment: #141 (comment)