Yes, the app should definitely reflect the car’s status.
Is everything else shown correctly on the phone (lock status, window status, climate status)? What happens in the car when you toggle sentry from the phone?
Maybe you should try rebooting your phone and restarting the touch display.
Another idea - it possible you are misinterpreting the icons at the top of the Tesla’s touchscreen?
The square rectangle with the red dot is not sentry mode, is is the dash cam. Sentry is the circle with lines radiating from it like a sun. If the dot is hollow, as in this picture, sentry is off. When sentry is active, the dot becomes red.
Not saying you have this wrong - just double checking….