🛠 Tooling: Add lychee-action workflow for checking site for broken external links

[cylewaitforit]

Tooling Report Checklist

• I have tried restarting my IDE and the issue persists.
• I have pulled the latest main branch of the repository.
• I have searched for related issues and found none that matched my issue.

Overview

While investigating #433, lychee was identified as a tool that may be useful in checking for broken external links. We can enable it in a workflow using lychee-action.

Additional Info

it feels like we also need to check the external links regularly, it looks like lychee can be run as an action https://github.com/lycheeverse/lychee-action .

Originally posted by @cylewaitforit in #447 (comment)

As for running Lychee as an action: that's an interesting one. I'm up for it if you are.

Originally posted by @JoshuaKGoldberg in #447 (comment)