I would find it very helpful to receive a system notification once the Assistant has finished its response. This is how the ChatGPT app works, and is especially nice for longer messages/more powerful models that can take a minute or longer to respond.
E.g., I send a prompt, leave the app, get a notification a few minutes later. When I open that notification, it should take me to the relevant thread and refresh it (if necessary) to show the full response.