Hyundia announced an EV with built in inverter, they call it Vehicle To Load[1]. Like you mention with a transfer switch your whole house could be a "load" For a non-emergency it probably makes sense to use a <70% depleted 2nd life battery, and save the new battery for transportation usage.

[1] https://www.hyundai.com/worldwide/en/company/newsroom/hyunda...

I didn't see anything in there about inverter output, other than it's pretty modest at 3.6 kW. My guess is it will do 120V, like most(all) built-in car inverters right now.

IMO, a good V2L setup needs to have split phase 240V in the US. But that would add significantly to the manufacturing cost of the car, so I won't hold my breath.

Most EV internal chargers are setup only for rectification. However, there's some slightly more expensive designs that would let it also act as an inverter. I believe this is what's spec'd for the Cybertruck.