Add unit tests for authentication API

[wisdomqin]

Description

The auth module (backend/app/api/auth.py) currently has no automated tests. Adding basic test coverage would improve code reliability.

What to do

1. Create backend/tests/test_auth.py
2. Add tests for key endpoints:
   • POST /api/auth/register — successful registration
   • POST /api/auth/login — successful login, wrong password
   • GET /api/auth/me — authenticated vs unauthenticated
3. Use pytest + httpx (already in dev dependencies)

Resources

• Auth router: backend/app/api/auth.py
• Test config: backend/pyproject.toml (asyncio_mode = auto)
• Run tests: cd backend && .venv/bin/pytest