As a relative nubee to SMB vans and electrical systems, I can't recommend this product too highly: Victron Smart Battery Monitor 712.
https://www.victronenergy.com/batter.../bmv-712-smart
It lets you see all that complex stuff that's going on, and you can set high and low-voltage alarms that will let you know when the house battery system is running low on juice. The Bluetooth app will show you just how much power that induction stovetop draws at startup and during use (often higher at startup), along with many other critical bits of information.
That said, you want all your appliances to be 12v when possible, including any fans you're running. We find our MaxxAire 4500 roof fan draws very little power, as does the 12v "dash fan" (with a long cord) we got on Amazon for cooling the bed area. Running the inverter even with no appliances turned on takes power, and you often lose up to 20% just changing the power (inverting) from 12v (your batteries) to 110.