OTOH, if you're replacing a gas furnace and already have A/C, then installing a new gas furnace + heat pump shouldn't cost much more than a new gas furnace + new A/C.
They likely exist, but none of my local residential HVAC companies carried them.
Electric resistive heating is not a suitable backup. If adopted at scale, it would tend to amplify demand spikes when the grid is at its most vulnerable.
They will pair to low ambient temperature capable condensers.
Daikin FXTQ series models
Mitsubishi SVZ series models
If you are searching.
I don't think having backup heat is a terrible idea, but it could be any fuel source. The fan should still function with minimal power to circulate air as long as there's some heat to move around.
People always forget the hot water. A GSHP usually has a de-superheater that can provide some heat during the shoulder seasons, but you can't rely on it and need the backup heat (as you do for the AUX heat for both when it's super-cold out and for the defrost cycle).