Something I noticed when trying to repro another issue:

% python
Python 3.8.13 (default, Mar 16 2022, 17:28:59)
[GCC 7.5.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import logging.handlers
>>> logging.handlers.SysLogHandler(address=("something-completely-bogus-doncha-know", 514))
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/usr/lib/python3.8/logging/handlers.py", line 829, in __init__
    ress = socket.getaddrinfo(host, port, 0, socktype)
  File "/usr/lib/python3.8/socket.py", line 918, in getaddrinfo
    for res in _socket.getaddrinfo(host, port, family, type, proto, flags):
socket.gaierror: [Errno -2] Name or service not known
>>>
Error in atexit._run_exitfuncs:
Traceback (most recent call last):
  File "/usr/lib/python3.8/logging/__init__.py", line 2127, in shutdown
    h.close()
  File "/usr/lib/python3.8/logging/handlers.py", line 892, in close
    self.socket.close()
AttributeError: 'SysLogHandler' object has no attribute 'socket'
% python3.9
Python 3.9.11 (main, Mar 16 2022, 17:27:06)
[GCC 7.5.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import logging.handlers
>>> logging.handlers.SysLogHandler(address=("something-completely-bogus-doncha-know", 514))
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/usr/lib/python3.9/logging/handlers.py", line 873, in __init__
    ress = socket.getaddrinfo(host, port, 0, socktype)
  File "/usr/lib/python3.9/socket.py", line 954, in getaddrinfo
    for res in _socket.getaddrinfo(host, port, family, type, proto, flags):
socket.gaierror: [Errno -2] Name or service not known
>>>
Error in atexit._run_exitfuncs:
Traceback (most recent call last):
  File "/usr/lib/python3.9/logging/__init__.py", line 2142, in shutdown
    h.close()
  File "/usr/lib/python3.9/logging/handlers.py", line 936, in close
    self.socket.close()
AttributeError: 'SysLogHandler' object has no attribute 'socket'

This is happening because logging.Handler is calling logging._addHandlerRef in logging.Handler.__init__ and _removeHandlerRef at exit via logging.shutdown(..).