I hate to use a competitor as an example - but Asana brings all tasks and conversations you are following and bring all the notifications into an inbox. It has an indicator if there are unread messages. Playing with Aha so far - it's hard for me to tell if there are new comments, todos, etc without having hundreds of emails - or constantly watching my activity page. Maybe I'm doing something wrong?
Example:
https://asana.com/guide/help/fundamentals/inbox