You can't tell at a quick glance if a user has read an internal message. Sure, you can click on the message to see who read it, but it would be nice if the blue dot on the icon is there if there is ANYTHING unread, including internal messages.

I just want to know "is this user up to date on this thread" - If the thread is "unread" on their end due to a message OR an email it should have the blue dot on the team icon view. If the distinction between emails and messages is necessary, maybe add another color?