I have all of the notifications set to on both in the Clickup desktop app and my mac's settings, but I don't get any notifications, chat or otherwise, on my desktop. I only get them on my mobile.

As others have requested, having a separate notification sound for chat would be great. Even better would be a separate Chat App, so that when I click a task link it opens in my main Clickup window, not in my chat window. You really need a separate experience.