Generate typehint for all the functions

[BoxiLi]

Currently, not all functions and classes in the codebase have type hints. In #255 and #256, I used an LLM to generate type hints, but the process was inefficient and cumbersome, as it required feeding each function individually (at least at that time, it does not handle long code very well). This approach makes it challenging to regenerate or update type hints when changes occur.

To improve this:

• It would be nice to have them automatically generated. We should use the modern syntax such as int | list[int] | None, as suggested in Add type hints to the circuit module #255. @gadhvirushiraj found MonkeyType, which will generate type hints based on the testing code.
• Those type hints added always need some post-processing. And we may find some small bugs while handling them. Therefore it is best to do this module by module, allowing for manageable PRs and manual adjustments.