Use type hints everywhere

Add type hints to all function signatures and class attributes:
- Enables static analysis with mypy/pyright
- Improves IDE autocompletion
- Documents expected types
- Catches type errors before runtime

```python
from typing import Optional

def process_user(user_id: int, name: str | None = None) -> dict[str, Any]:
...

class UserService:
def __init__(self, repo: UserRepository) -> None:
self.repo = repo
```