Exceptions don't match CPython `requests` that closely

The CPython `requests` library has its own set of exceptions: https://requests.readthedocs.io/en/latest/api/#requests.ConnectTimeout
which are subclasses of system exceptions. Here is the source, showing the class definitions:
https://requests.readthedocs.io/en/latest/_modules/requests/exceptions/

I think using some subset of the `requests` exceptions might be nice for writing compatible code and one with clearer exceptions.

Start by reviewing the CPython requests exception definitions and the linked ConnectTimeout API documentation, then compare them with this library’s current exception behavior. The issue does not specify which exceptions or compatibility rules to implement; done would require a decided subset and corresponding behavior that supports clearer, requests-compatible error handling.

Written by the indexing model from the issue text.