Add broken link checking Action

Also adjusts the entire workflow to only run if a PR or push contains changes to a markdown file

.github/workflows/lint-docs.yml

@@ -4,16 +4,49 @@ on:
   workflow_dispatch:
   push:
     branches: [ main, linux ]
+    paths:
+      - '**.md'
   pull_request:
     branches: [ main, linux ]
+    paths:
+      - '**.md'
 
 jobs:
   lint-markdown:
     name: Lint markdown files
     runs-on: ubuntu-latest
     steps:
-      - uses: actions/checkout@dcd71f646680f2efd8db4afa5ad64fdcba30e748
+      - uses: actions/checkout@2541b1294d2704b0964813337f33b291d3f8596b
 
       - uses: DavidAnson/markdownlint-cli2-action@744f913a124058ee903768d3adb92a4847e5d132
         with:
           globs: "**/*.md"
+
+  check-links:
+    name: Check for broken links
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@2541b1294d2704b0964813337f33b291d3f8596b
+
+      - name: Run link checker
+        # For any troubleshooting, see:
+        # https://github.com/lycheeverse/lychee/blob/master/docs/TROUBLESHOOTING.md
+        uses: lycheeverse/lychee-action@f1da3291e1d03cbe11a413ae9f16b62fec99e6b6
+
+        with:
+          # user-agent: if a user agent is not specified, some websites (e.g.
+          # GitHub Docs) return HTTP errors which Lychee will interpret as
+          # a broken link.
+          # no-progress: do not show progress bar. Recommended for
+          # non-interactive shells (e.g. for CI)
+          # inputs: by default (.), this action checks files matching the
+          # patterns: './**/*.md' './**/*.html'
+          args: >-
+            --user-agent "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/100.0.4896.75 Safari/537.36"
+            --no-progress .
+          fail: true
+        env:
+          # A token is used to avoid GitHub rate limiting. A personal token with
+          # no extra permissions is enough to be able to check public repos
+          # See: https://github.com/lycheeverse/lychee#github-token
+          GITHUB_TOKEN: ${{secrets.GITHUB_TOKEN}}