Additional settings-related features and issues within Microsoft Teams for Education
I believe this is a bug on how teams handles the notification icon with Windows. As @Ruwim.B pointed out, the presence status shows on the taskbar as well. However, it only shows up when the"Taskbar size" is set to Default. When the taskbar is set to small it can only show a small dot next to app icons with notifications, and I think that the presence status is interpreted as a notification.
When I change my presence the taskbar icon does flicker, so I assume it is updating it even when small.
I tried all of the other recommendations, and unless there is a way to disable the presence icon showing I think this will have to be handled on Microsoft's end.
Please let me know if anyone else has ideas because it is still very annoying!