[3.14] gh-91555: add warning to docs about possibility of deadlock/infinite recursion (GH-135954) (GH-135988)

(cherry picked from commit a4625d5)

Author: miss-islington

Doc/library/logging.handlers.rst

@@ -1059,6 +1059,15 @@ possible, while any potentially slow operations (such as sending an email via
    .. note:: If you are using :mod:`multiprocessing`, you should avoid using
       :class:`~queue.SimpleQueue` and instead use :class:`multiprocessing.Queue`.
 
+   .. warning::
+
+      The :mod:`multiprocessing` module uses an internal logger created and
+      accessed via :meth:`~multiprocessing.get_logger`.
+      :class:`multiprocessing.Queue` will log ``DEBUG`` level messages upon
+      items being queued. If those log messages are processed by a
+      :class:`QueueHandler` using the same :class:`multiprocessing.Queue` instance,
+      it will cause a deadlock or infinite recursion.
+
    .. method:: emit(record)
 
       Enqueues the result of preparing the LogRecord. Should an exception