we should NOT be losing all battery power within a few days with the fridge on Auto and nothing else on
Wrong
Turn the fridge off, for testing your battery problem, unplug the 120v cord at the back of the fridge
The 12v controls draw very little power
But if it's running from the inverter, you are using about 30amps draw on the 12v
The electric heating elements in an RV fridge are around 340 watts of power, that's 3 amps on Shore power , but takes 30 amps 12v power into the inverter to make 3 amps at 120v
Plus conversion losses