GolanB, I will get back to you after my next charge.
I did not run the Tesla app at all after my last charge and as expected, after 36 hours, I still have 25% charge left, which equates to what I originally described; 48 hours of battery time.
After I charge tomorrow, I will open the Tesla app. I don't recall if I kept it running in the background or not, but 10.5 hours after finishing the charge, my phone said it used 3% battery, but was running 10.5 hours. I am pretty sure I closed it with a swipe. I finally force stopped it after that.
Generally I am not within range of my car when not driving. The front screen notification says Tesla disconnected.
I normally terminate the app, but I don't go in that often.
I can safely say uninstalling the app won't have an effect since not using the app at all gave me the same length of battery as before I got the car.