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

script/check-links

@@ -0,0 +1,7 @@
+#!/usr/bin/env bash
+
+set -euo pipefail
+
+cargo install lychee
+cd "$(dirname "$0")/.."
+lychee --no-progress './docs/src/**/*'