I belive the python traceback module was designed to produce the same output as the internal exception printer (sys.__excepthook__), but this is not the case when the exception's __str__ raises an exception.

Given an exception of the following class:
class E(Exception):
   def __str__(self):
      raise RuntimeError

Internal printer output:
Traceback (most recent call last):
  File "inconsistent.py", line 6, in <module>
    raise E()
__main__.E: <exception str() failed>

traceback.print_exc output:
Traceback (most recent call last):
  File "inconsistent.py", line 6, in <module>
    raise E()
E: <unprintable E object>

New changeset 9e31b3952f6101ef71ec029481b972169ab0e0f1 by Irit Katriel in branch 'main':
bpo-41031: Match C and Python code formatting of unprintable exceptions and exceptions in the __main__ module. (GH-28139)
https://github.com/python/cpython/commit/9e31b3952f6101ef71ec029481b972169ab0e0f1