Use async database operations

Use async database drivers with FastAPI:
- asyncpg for PostgreSQL
- SQLAlchemy 2.0 async mode
- databases package for simple queries

```python
from sqlalchemy.ext.asyncio import create_async_engine, AsyncSession

engine = create_async_engine(
"postgresql+asyncpg://user:pass@localhost/db",
echo=True,
)

async def get_user(db: AsyncSession, user_id: int) -> User | None:
result = await db.execute(
select(User).where(User.id == user_id)
)
return result.scalar_one_or_none()
```