Catch unhandled exception in websocket_api (#42693)

Co-authored-by: springstan <46536646+springstan@users.noreply.github.com>
Co-authored-by: Paulus Schoutsen <balloob@gmail.com>

homeassistant/components/websocket_api/http.py

@@ -222,11 +222,11 @@ class WebSocketHandler:
                 self._to_write.put_nowait(None)
                 # Make sure all error messages are written before closing
                 await self._writer_task
-            except asyncio.QueueFull:
+                await wsock.close()
+            except asyncio.QueueFull:  # can be raised by put_nowait
                 self._writer_task.cancel()
 
-            await wsock.close()
-
+            finally:
                 if disconnect_warn is None:
                     self._logger.debug("Disconnected")
                 else: