Use lychee link checker instead of linkinator (#5868)

Seems like linkinator doesn't find any files:
https://github.com/emilk/egui/pull/5853#issuecomment-2765526298

This will check all links in .md files (except CHANGELOG.md) and in toml
files

.github/workflows/spelling_and_links.yml

@@ -15,16 +15,20 @@ jobs:
       - name: Check spelling of entire workspace
         uses: crate-ci/typos@master
 
-  linkinator:
-    name: linkinator
+  lychee:
+    name: lychee
     runs-on: ubuntu-latest
     steps:
       - uses: actions/checkout@v4
-      - uses: jprochazk/linkinator-action@main
-        with:
-          linksToSkip: "https://crates.io/crates/.*, http://localhost:.*" # Avoid crates.io rate-limiting
-          retry: true
-          retryErrors: true
-          retryErrorsCount: 5
-          retryErrorsJitter: 2000
+      - name: Don't check CHANGELOG.md files
+        # This is really stupid but lychee doesn't have a way of excluding files via GLOB:
+        # https://github.com/lycheeverse/lychee/issues/1608
+
+        # We need to exclude CHANGELOG.md since we don't want to have a CI failure everytime some contributor decides
+        # to change their username.
+        run: rm -r  */**/CHANGELOG.md CHANGELOG.md
+      - name: Link Checker
+        uses: lycheeverse/lychee-action@v2
+        with:
+          args: "'**/*.md' '**/*.toml' --exclude localhost --exclude reddit.com" # I guess reddit doesn't like github action IPs