[rh] Remove additional logging handlers on close (#9032)

Fixes https://github.com/yt-dlp/yt-dlp/issues/8922

Authored by: coletdjnz

yt_dlp/networking/_websockets.py

@@ -90,10 +90,12 @@ class WebsocketsRH(WebSocketRequestHandler):
 
     def __init__(self, *args, **kwargs):
         super().__init__(*args, **kwargs)
+        self.__logging_handlers = {}
         for name in ('websockets.client', 'websockets.server'):
             logger = logging.getLogger(name)
             handler = logging.StreamHandler(stream=sys.stdout)
             handler.setFormatter(logging.Formatter(f'{self.RH_NAME}: %(message)s'))
+            self.__logging_handlers[name] = handler
             logger.addHandler(handler)
             if self.verbose:
                 logger.setLevel(logging.DEBUG)
@@ -103,6 +105,12 @@ class WebsocketsRH(WebSocketRequestHandler):
         extensions.pop('timeout', None)
         extensions.pop('cookiejar', None)
 
+    def close(self):
+        # Remove the logging handler that contains a reference to our logger
+        # See: https://github.com/yt-dlp/yt-dlp/issues/8922
+        for name, handler in self.__logging_handlers.items():
+            logging.getLogger(name).removeHandler(handler)
+
     def _send(self, request):
         timeout = float(request.extensions.get('timeout') or self.timeout)
         headers = self._merge_headers(request.headers)