gh-135660: Print the exception raised in _safe_string

[Locked-chess-official]

effect:

Python 3.15.0a0 (heads/main-dirty:5776d0d2e08, Oct 12 2025, 00:07:14) [MSC v.1944 64 bit (AMD64)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> class WrongException1(Exception):
...     def __str__(self):
...         raise WrongException2()
...     __repr__ = __str__
...
>>> class WrongException2(Exception):
...     def __str__(self):
...         raise WrongException1()
...     __repr__ = __str__
...
>>> a = WrongException1()
>>> a.__notes__ = WrongException2()
>>> b = a.__notes__
>>> raise a
Traceback (most recent call last):
  File "<python-input-5>", line 1, in <module>
    raise a
WrongException1: <exception str() failed>
<__notes__ repr() failed>

Exception ignored in exception str():
Traceback (most recent call last):
  File "C:\Users\hh180\my_python\handle_keyerror\Lib\traceback.py", line 288, in _safe_string
    return func(value)
  File "<python-input-0>", line 3, in __str__
    raise WrongException2()
WrongException2: <exception str() failed>

Exception ignored in exception str():
Traceback (most recent call last):
  File "C:\Users\hh180\my_python\handle_keyerror\Lib\traceback.py", line 288, in _safe_string
    return func(value)
  File "<python-input-1>", line 3, in __str__
    raise WrongException1()
WrongException1: <exception str() failed>

Exception ignored in __notes__ repr():
Traceback (most recent call last):
  File "C:\Users\hh180\my_python\handle_keyerror\Lib\traceback.py", line 288, in _safe_string
    return func(value)
  File "<python-input-1>", line 3, in __str__
    raise WrongException1()
WrongException1: <exception str() failed>

Exception ignored in exception str():
Traceback (most recent call last):
  File "C:\Users\hh180\my_python\handle_keyerror\Lib\traceback.py", line 288, in _safe_string
    return func(value)
  File "<python-input-0>", line 3, in __str__
    raise WrongException2()
WrongException2: <exception str() failed>
>>> assert b is a.__notes__
>>>

If the change break some test, I will try to fix it.
This is the attempt for add the note in handling.
If it is success, we then can use "exception_target" to print the exception from handling as warnings.

• Issue: KeyError hides the exception raised by str(key) #135660

[Locked-chess-official]

Now it seems that the test for traceback._safe_str need to be update. However, I'll have a sleep now.

[StanFromIreland]

This PR has hundreds of cosmetic changes (I assume you linted the code with black or the like?), resulting in a diff of +663/-244, please revert them all.