Build the documentation in CI (#734)

To ensure things are working! The `--strict` flag performs checks for
valid URLs and such.

.github/workflows/ci.yaml

@@ -96,3 +96,29 @@ jobs:
             git status --porcelain
             exit 1
           fi
+
+  docs:
+    timeout-minutes: 10
+    name: "mkdocs"
+    runs-on: ubuntu-latest
+    env:
+      MKDOCS_INSIDERS_SSH_KEY_EXISTS: ${{ secrets.MKDOCS_INSIDERS_SSH_KEY != '' }}
+    steps:
+      - uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683 # v4.2.2
+        with:
+          fetch-depth: 0
+          persist-credentials: false
+      - uses: astral-sh/setup-uv@bd01e18f51369d5a26f1651c3cb451d3417e3bba # v6.3.1
+      - uses: actions/setup-python@a26af69be951a213d495a4c3e4e4022e16d87065 # v5.6.0
+      - name: "Add SSH key"
+        if: ${{ env.MKDOCS_INSIDERS_SSH_KEY_EXISTS == 'true' }}
+        uses: webfactory/ssh-agent@a6f90b1f127823b31d4d4a8d96047790581349bd # v0.9.1
+        with:
+          ssh-private-key: ${{ secrets.MKDOCS_INSIDERS_SSH_KEY }}
+
+      - name: "Build docs (public)"
+        run: uvx --with-requirements docs/requirements.txt mkdocs build --strict -f mkdocs.public.yml
+
+      - name: "Build docs (insiders)"
+        if: ${{ env.MKDOCS_INSIDERS_SSH_KEY_EXISTS == 'true' }}
+        run: uvx --with-requirements docs/requirements-insiders.txt mkdocs build --strict -f mkdocs.insiders.yml