feat: add FastAPI app factory and health check endpoint

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

tests/test_app.py

@@ -0,0 +1,12 @@
+"""Tests for the FastAPI application factory."""
+
+from fastapi.testclient import TestClient
+
+
+class TestCreateApp:
+    """Tests for the application factory and basic setup."""
+
+    def test_app_starts_without_error(self, client: TestClient) -> None:
+        """The app should initialize and serve requests."""
+        response = client.get("/health")
+        assert response.status_code == 200