Furnaces don’t come with batteries because a 12v 100Ah battery that costs $180 will run a 1/3rd HP (700w) fan for 2 hours. To sustain the fan for 3 days, you’d need 36 batteries. Lead-acid batteries have a limited lifespan. You would also need a transfer switch and enclosures and at that point you may as well buy a UPS or a natural gas generator to provide backup power.
One thing the NEC 2020 update allowed is bi-directional power between an EV and its charger, you can set up an EV to provide backup power your house, with a transfer switch and everything.
Radiant heating systems with boilers require electricity for the pump, even if they’re gas fired. Electric resistive heating needs electricity. Forced air heating needs electricity to run the fan. All heating systems require electric power, even if the heat is generated by burning natural gas.
We're talking about forced air furnaces here, I think. Something has to force the air. A big blower motor that takes hundreds of watts.
Forced air heat is not great in terms of comfort, but in Texas you already have all the ductwork and the blower motor and so on for AC, so it's simplest just to add a gas burner to that.