It would be nice if the system tray icon changed when there are one or more unread private messages.

Here's a riot icon for reference:
https://i.imgur.com/ipkBCj3.png

The fact that it shows the number of unread chats is perhaps nice, but not necessary. A binary status icon is just fine in my book.

Reason for this:
It lets one know at a glance if any PMs were missed while away from the PC. The red color in the image example given also draws the eye which I personally like.

Good idea