Add docstrings, refactor process_query, and move AsyncTimeoutError to gitingest.exceptions

[filipchristiansen]

This PR introduces two main changes:

1. Adds docstrings to various functions to improve code documentation and readability.
2. Moves the main function process_query to the top of the process_query.py file for better organization.
3. Prefixes helper functions with an underscore to follow Python naming conventions for internal functions.
4. Moves the AsyncTimeoutError exception to the gitingest.exceptions module for better exception handling organization.

These changes enhance code clarity, maintainability, and adhere to best practices in Python code organization and exception management.

[cyclotruc]

Thank you, the new docstrings are very much welcome