Currently if I am in a chat and another applications' window comes up in front of Teams (i.e., Teams is no longer visible), I do not get a notification in my icon tray when the person I was chatting with responds. This leads me to missing a response for sometimes up until hours later when I go back to Teams to chat with someone else or view a different notification.
I like that you don't get the notification when it is the active chat and it is visible. However, if Teams is not visible, it should notify of a new message.
Al Whitnah commented
It would be nice for this to function like Skype.
When MS-TEAM is minimized and a new Chat arrives the icon should flash in the taskbar or system tray.
As it currently stands you must be viewing TEAMS; where a number is listed below the "chat" icon.
For this reason I miss messages and the by the the time I respond the person is offline.
My company, Thomson Reuters, recently switched from using WebEx Teams to Microsoft Teams. With WebEx teams it put a notification number on the Windows Taskbar icon letting you know how many chat messages you had missed. We really liked that feature and would love it if Microsoft Teams would do that. The activity notification number is helpful, but when you have the chat window closed/minimized that isn't so helpful.