Interesting. There are clearly other failures going on here.
First using the "off grid" mode enabled from the app is not truly off grid. It's merely a simulation. You are not actually off grid. As long as the simulation doesn't fail, the Powerwall(s) will provide enough energy to prevent you from using the grid. The simulation will end if the TEG detects a PW malfunction or the charge level goes too low. The simulation doesn't actually physically disconnect the breaker in the TEG so if there's even an undetected failure and the PWs can't keep up, then the balance comes from the grid. The simulation also can't test forcing solar off when the PWs fill up because the way that works is the PWs change their line frequency to signal the inverters to shut down but in the simulation, the line frequency is still the grid.
A brownout isn't even possible unless the utility experienced a brownout at the same time since you are not actually disconnected from the grid.
If you disconnected by using the main service breaker, then of course anything is possible if the Powerwalls are truly malfunctioning.
Secondly, the TEG has a backup cellular modem. I was at first confused why the app still all worked for the tesla energy functions whenever my Comcast went out and turns out it's because there's an AT&T modem. Thirdly, you don't even need that to reconnect. To even enable the off-grid simulation button, you had to pair your phone to the PWs which allows you to access certain functionality like off-grid even if there's no internet connection, but you need to be close enough to the TEG for that.
Lastly, you didn't quite do what I intended. The idea was to turn everything off in the house, go off-grid, and then add load back until you exceeded 1.0 kw to see if you could get your PWs to do that. In off grid simulation mode, the simulation would end if the PWs decided they'd hit their max. In true off grid mode, with the main breaker off, the PWs would at some point reset. If just over 1.0 kw worked, continue adding load to test it. I certainly didn't mean add one huge load all at once and an AC that runs 2.5 kw continuous will pull WAY more than that at startup even with a slow start capacitor installed.
When you first had the system installed, one of the first things to test before you pay for anything is to throw the main service breaker and start up all HVACs that are backed up by the system to make sure they start without resetting the PWs.