Enable the bad-exit-annotation ruff rule and fix related warnings

[correctmost]

PR Description:

This commit is a backwards compatible alternative to #3562.

References:

Typeshed definition for __exit__

https://github.com/python/typeshed/blob/8a6bfb06981a9bab7c74472f62d6132f501c4a0e/stdlib/contextlib.pyi#L52-L54

__exit__ docs

If an exception is supplied, and the method wishes to suppress the exception (i.e., prevent it from being propagated), it should return a true value. Otherwise, the exception will be processed normally upon exit from this method.

-- Python docs

Tests and Checks

• I have tested the code!