ci: Restore lychee link check. Only validate internal links (#32463)

Follow-up to: https://github.com/zed-industries/zed/pull/32460
Follow-up to: https://github.com/zed-industries/zed/pull/30844

Release Notes:

- N/A

.github/actions/build_docs/action.yml

@@ -19,6 +19,12 @@ runs:
       shell: bash -euxo pipefail {0}
       run: ./script/linux
 
+    - name: Check for broken links
+      uses: lycheeverse/lychee-action@82202e5e9c2f4ef1a55a3d02563e1cb6041e5332 # v2.4.1
+      with:
+        args: --no-progress --exclude '^http' './docs/src/**/*'
+        fail: true
+
     - name: Build book
       shell: bash -euxo pipefail {0}
       run: |

script/check-links

@@ -2,6 +2,31 @@
 
 set -euo pipefail
 
+usage() {
+    echo "Usage: $0 [local|all] [--help]"
+    echo "  local  Only check local links (default)"
+    echo "  all    Check all links including remote ones"
+    exit 1
+}
+
+check_mode="local"
+if [ $# -eq 1 ]; then
+    case "$1" in
+    "local") check_mode="local" ;;
+    "all") check_mode="all" ;;
+    "--help") usage ;;
+    *) echo "Invalid argument: $1" && usage ;;
+    esac
+else
+    usage
+fi
+
 cargo install lychee
 cd "$(dirname "$0")/.."
-lychee --no-progress './docs/src/**/*'
+
+if [ "$check_mode" = "all" ]; then
+    lychee --no-progress './docs/src/**/*'
+else
+    lychee --exclude '^http' './docs/src/**/*'
+fi
+#