Add E2E tests, fix bugs

Made-with: Cursor

e2e/tests/test_health.py

@@ -0,0 +1,7 @@
+def test_health_returns_200(base_url, api_client):
+    # Act
+    response = api_client.get(f"{base_url}/health")
+
+    # Assert
+    assert response.status_code == 200
+    assert response.json()["status"] == "healthy"