You have 12v only powered items, propane only items, 120v items and some that work on multiple inputs.
12v only: Furnace motor, water pump, lights, front and rear jacks, ceiling fans (Maxxfan and bath fan), TV and Furrion stereo. These items only work off of your batteries.
120v only: AC, microwave.
Propane only: cook top
Combination: Water heater (heats on propane or 120v or both at the same time), Fridge (on shore power it defaults to 120v, no shore power it goes to propane, if you want to run on 12v you have to select, at least on my 3 way Dometic. It’s most efficient on propane).
Your furnace generates heat from propane only but the fan is 12v only, no shore power needed. Also, if you have the 2K watt inverter it works on 12v to generate 120v, if your batteries don’t have sufficient charge your inverter will not function properly.
Hope this helps. Mike