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….
In my experience with my model 3, the off/on toggle doesn't update to match current status when you switch sentry mode with your phone app or with the top right icon shortcut. Overlooked bug I guess that always stays stuck with whatever it was last set to, so it isn't a reliable indicator to see whether Sentry mode is on or not (better to just look for if the red dot is visible or not)