As far as I could tell from using usermin 2.102's webmail interface, it does not prompt / request privileges to emit notifications, and presumably does not try emitting any notifications (unlike VirtualMin, which is able to do that when it has software updates available for example).
If my observation is correct (as I have not seen it working), then it would be quite useful to implement https://developer.mozilla.org/en-US/docs/Web/API/Notifications_API/Using_the_Notifications_API for usermin's webmail interface. Particularly for the inbox folder, and any other folder that the user might currently be viewing but unfocused (i.e. the user has switched to another tab / window / workspace).