Add mypy type check for uv-python scripts (#5332)

## Summary

Per https://github.com/astral-sh/uv/pull/4853#issuecomment-2212505407

> If we're going to aim for full type coverage, we should probably
follow this by adding type checking in CI too otherwise it seems too
easy for it to become out of date.

.github/workflows/ci.yml

@@ -59,14 +59,27 @@ jobs:
       - name: "Prettier"
         run: npx prettier --check "**/*.{json5,yaml,yml}"
 
+      - name: "README check"
+        run: python scripts/transform_readme.py --target pypi
+
+  python-lint:
+    name: "Python lint"
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+
+      - uses: actions/setup-python@v5
+        with:
+          python-version: 3.12
+
       - name: "Ruff format"
         run: pipx run ruff format --diff .
 
       - name: "Ruff check"
         run: pipx run ruff check .
 
-      - name: "README check"
-        run: python scripts/transform_readme.py --target pypi
+      - name: "Mypy check"
+        run: pipx run --python 3.12 mypy
 
   cargo-clippy:
     needs: determine_changes