Add comprehensive unit and integration test coverage to both the backend (FastAPI/Python) and frontend (React/TypeScript). The project currently has zero tests — pytest is configured in pyproject.toml with pytest-asyncio and httpx, but no actual test files exist. The frontend has no test tooling at all.
**Scope:**
- Unit tests for isolated logic (schemas, services, utilities)
- Integration tests for API endpoints (using httpx AsyncClient against a test database)