ci: Move lychee link check to script/check-links (#32460)

Follow-up to: https://github.com/zed-industries/zed/pull/30844

Transient link failure was blocking PR tests passing. [Example
run](https://github.com/zed-industries/zed/actions/runs/15560960788/job/43812878693?pr=32458).

Release Notes:

- N/A
46f98b6001Peter Tripp committed on 6/10/2025, 2:11:24 PM· committed by GitHubparentc1a4a24
3 files changedLine totals unavailable