class Some_Class:

    def error(self):
        if not getattr(self, 'boo', None):
            raise Exception(f'`class {self.__class__.__name__}:` raised some error!')


something = Some_Class()
something.error()


# This is how Error looks
# -----------------------
Traceback (most recent call last):
  File "/test.py", line 9, in <module>
    something.error()
  File "/test.py", line 5, in error
    raise Exception(f'`class {self.__class__.__name__}:` raised some error!')
Exception: `class Some_Class:` raised some error!


# This is how Error should look
# -----------------------------
Traceback (most recent call last):
  File "/test.py", line 9, in <module>
    something.error()
  File "/test.py", line 5, in error
    raise Exception(...)
Exception: `class Some_Class:` raised some error!


When a developer manually raises an error they want the user/developer debugging the error to see the final, nicely formatted error message itself "Exception: `class Some_Class:` raised some error!" not the ugly formating of the error message itself "raise Exception(f'`class {self.__class__.__name__}:` raised some error!')" which can also lead to confusion, thus it should be hidden as "raise Exception(...)"

It could also be said that "raise Exception(...)" shouldn't even be shown but what raises this error condition "if not getattr(self, 'boo', None):" but this seems more work so i am keeping it simple by saying lets just hide the ugly formatting part.

This sounds like it needs at least some discussion on python-ideas. For example, just reading your description I can't imagine what is supposed to happen when an error occurs when producing argument to the exception.