In Odoo 16, the live chat widget uses websockets to communicate with the server and update the conversation in real-time. If the conversation is not being automatically updated, it is possible that there is an issue with the websocket connection or with the live chat server.
There are a few things you can try to troubleshoot this issue:
Check the logs for any error messages related to the live chat widget or websockets. This will give you a clue about what might be causing the problem.
Make sure that the live chat server is running and that the correct configuration is being used. You can check the live chat configuration in the "Live Chat" menu under "Settings" in the backend.
Check that the websocket connection is being established correctly. You can use a tool like websocket.org to test the connection and see if there are any issues.
If you are using a firewall or security tool, make sure that it is not blocking the websocket connection.
I hope this helps. Let me know if you have any questions or if you need further assistance.