While the activityBackgroundTint modifier is intended to set the background color of a Live Activity, it often fails to dynamically update, leaving the activity with an incorrect background. Replacing it with
ZStack { Color(.background) .... }
solves the problem, but this is a workaround. The activityBackgroundTint modifier is still needed, at a minimum, so that the "Allow Live Activity for the app" extension does not have the default color.