Increase websocket_api allowed peak time to 10s (#141680)

* Increase websocket_api allowed peak time to 10s

fixes #141624

During integration reload or startup, we can end up sending a message for
each entity being created for integrations that create them from an external
source (ie MQTT) because the messages come in one at a time. This can overload
the loop and/or client for more than 5s. While we have done significant work
to optimize for this path, we are at the limit at what we can expect clients
to be able to process in the time window, so increase the time window.

* adjust test

homeassistant/components/websocket_api/const.py

@@ -21,7 +21,7 @@ type AsyncWebSocketCommandHandler = Callable[
 DOMAIN: Final = "websocket_api"
 URL: Final = "/api/websocket"
 PENDING_MSG_PEAK: Final = 1024
-PENDING_MSG_PEAK_TIME: Final = 5
+PENDING_MSG_PEAK_TIME: Final = 10
 # Maximum number of messages that can be pending at any given time.
 # This is effectively the upper limit of the number of entities
 # that can fire state changes within ~1 second.

tests/components/websocket_api/test_http.py

@@ -241,7 +241,7 @@ async def test_pending_msg_peak(
     instance: http.WebSocketHandler = cast(http.WebSocketHandler, setup_instance)
 
     # Fill the queue past the allowed peak
-    for _ in range(10):
+    for _ in range(20):
         instance._send_message({"overload": "message"})
 
     async_fire_time_changed(
@@ -251,7 +251,7 @@ async def test_pending_msg_peak(
     msg = await websocket_client.receive()
     assert msg.type is WSMsgType.CLOSE
     assert "Client unable to keep up with pending messages" in caplog.text
-    assert "Stayed over 5 for 5 seconds" in caplog.text
+    assert "Stayed over 5 for 10 seconds" in caplog.text
     assert "overload" in caplog.text