EV Play has three separate subsystems: The screen module, the Android module, and the Android Auto/CarPlay ("AA/CP") module. Whenever you exit the vehicle and/or lock the doors, EV Play will shutdown the Android and AA/CP systems after a few minutes. The screen module still is powered, so that the screen can show GearGuard Gary while the doors are locked, and immediately show the Rivian screen as soon as you unlock and/or open the doors.
When you unlock and/or open the doors, EV Play will then boot up, which takes about 20 seconds. At that point switching becomes available, as well as AA/CP.
To note, the screen system takes a very, very, very small amount of power. Essentially at a full charge, it would take approximately 50 years to drain the battery.