We love clickup notifications because of the notification stream, that is less disruptive of your work and you can work through notifications similar to an inbox and can clear the notifications.
In parallel, we use an external chat tool which is "disrupting" your work similar to a phone call for urgent requests. Now the problem is that clickup chats go into the same "work pipeline" of notifications as all the notifications. Hence, they are not really serving their "high priority" purpose.
To address this, my suggestion would be:
  1. Show a notification bubble on tasks in the tray (or allow this to be turned on)
  2. Allow chat views to be sent to the tray and then give them a notification bubble.
Alternatively you could also give us a separate notification view for chats or a chat view similar to the central doc view. In all implementations it is important that from the main view you can see your chat notifications and that these are separated from the normal notifications.