I think this is most of the way to what the future looks like: a high efficiency heat pump with cogeneration, so you can still burn propane or natural gas for heat and limited power to drive the heating system in an emergency (and if you don't have gas service to the premises, you have either a propane tank [1] or an exterior outlet to hook up outside). You must have a solution for when utility power is down for substantial periods of time.

During the winter storm that just passed, a friend in the Midwest called that their house had no power and was rapidly cooling. The utility could provide no ETA to resolution. I walked them through (over the phone) safely enough backfeeding enough power from a gasoline generator (outside, with the extension cord run through a basement escape window) into their furnace circuit to bootstrap the furnace (and run the blower fan) to keep the house warm so that the pipes didn't freeze and burst. If the HVAC system had had a small battery and some way to generate power from the heat it was burning, the gasoline generator would've been unnecessary. Perhaps an integrated thermoelectric generator [2]? A standby generator isn't financially practical for most folks ($6k + install).

(EDIT: to the safety folks out there possibly concerned, the furnace breaker and main breaker were tripped, and the meter was pulled to prevent any chance of harm to electrical linemen from inadvertently energizing the utility line; take no chances with safety, do not attempt this at home)

[1] https://www.amerigas.com/about-propane/propane-tank-sizes

[2] https://patents.google.com/patent/US5427086A/en