Add type checking using Pyrefly

.github/workflows/ci.yml

@@ -33,6 +33,19 @@ jobs:
     - uses: actions/checkout@v6
     - uses: actions/setup-python@v6
     - uses: pre-commit/action@v3.0.1
+  type-checking:
+    runs-on: ubuntu-latest
+    steps:
+    - uses: actions/checkout@v6
+    - uses: actions/setup-python@v6
+      with:
+        # Run type checking against the oldest supported version
+        python-version: "3.10"
+    - uses: astral-sh/setup-uv@v7
+      with:
+        enable-cache: true
+    - run: uv sync --all-extras
+    - run: uv run pyrefly check --output-format=github
   core:
     needs: [pre-commit]
     uses: OpenAstronomy/github-actions-workflows/.github/workflows/tox.yml@v2