Two questions about this mechanism:
Firstly, is it supposed to include the ‘help chat’ in the count. It doesn’t do so (for me). Similarly for the site-supporters chat. It’s the help chat that I think would particularly benefit from being included, allowing regular users to more readily help new users and each other.
Secondly and less importantly, the count appears to be device specific. If you’ve read the chat on any device then you don’t need to be alerted to it for other devices.