Convert markdown check to lychee

.github/workflows/reusable-markdown-link-check.yml

@@ -12,13 +12,11 @@ jobs:
     steps:
       - uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683 # v4.2.2
 
-      - name: Install markdown-link-check
-        # TODO(jack-berg): use latest when config file reading bug is fixed: https://github.com/tcort/markdown-link-check/issues/246
-        run: npm install -g [email protected]
-
-      - name: Run markdown-link-check
-        run: |
-          find . -type f \
-                 -name '*.md' \
-                 -not -path './CHANGELOG.md' \
-               | xargs .github/scripts/markdown-link-check-with-retry.sh
+      - uses: lycheeverse/lychee-action@f613c4a64e50d792e0b31ec34bbcbba12263c6a6 # v2.3.0
+        with:
+          # excluding links to pull requests and issues is done for performance
+          args: >
+            --include-fragments
+            --exclude "^https://github.com/open-telemetry/opentelemetry-java-contrib/(issue|pull)/\\d+$"
+            --max-retries 6
+            .