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I see the same in Python 3.10 on windows 10.
If I change the relative imports to absolute imports in a couple of functions in multiprocessing.context as below, the attached (pool_error_on_3.9.py) script not longer raises the exception.
 def SimpleQueue(self):
 '''Returns a queue object'''
 from multiprocessing.queues import SimpleQueue
 return SimpleQueue(ctx=self.get_context())
 def Pool(self, processes=None, initializer=None, initargs=(),
 maxtasksperchild=None):
 '''Returns a process pool object'''
 from multiprocessing.pool import Pool
 return Pool(processes, initializer, initargs, maxtasksperchild,
 context=self.get_context())