The ford home integration setup never really worked as advertised. The idea is that if the home power fails, the truck will output high voltage DC to an inverter that powers the house. No owners have got this failing over reliably.
Most people just plug an extension cord into the onboard inverter. You have to manually flip it on and plug it in, but 240V30A is plenty for an emergency. Doing it this way isn't any different from any other vehicle with an onboard inverter though.
It's completely illegal unless your home has a "transfer switch" (manual or automatic) installed for this purpose - and if you're plugged into the generator side of a transfer switch, then you can't charge the truck, only discharge it. There are probably modules designed for solar power that allow two-way transfer safely.
On the other hand there are no tricky rules for an electric truck to have extra power outlets in it.
I'd expect a lot of people might just use extension cords and plug critical devices directly into the truck.
As you should. That's a good way to handle emergency use. Much easier and safer than rewiring your house.
Bingo. Unsurprisingly, the ford system is basically an off the shelf solar system minus the panels and with a very tiny battery to kickstart the system.
Do cybertrucks work any differently?
I believe they use the vehicle's onboard inverter rather than an external one.