I have a Prius. It is a plug in with 4kW of power in the traction battery, much more than the standard Prius but the principal is the same for both.

The car is not shut down, it acts as a generator to charge the battery when the battery is run down, turning on and off as necessary.

There are two ways to access the power. Tap the 200V plus (different models use slightly different voltages) battery and use an inverter that takes in 200+V and supplies the AC of your choice, 230V in the UK. This is expensive and specialist but doable.

Or, better, put a high current socket across the 12V battery (I use Anderson Powerpoles) and plug in a 12Vdc to 230Vac inverter when needed. Cheap and simple.

The 200+Vdc traction battery charges the 12DC accessory battery via a DC/DC inverter whilst the car is turned on (in 'Ready') and, with the right cable and socket the 12Vdc battery may supply 100A but it is prudent to only take 50 or 60A, so approximately 750W is available continuously.

When the 200+V traction battery is low the engine starts automaticly and tops it back up then turns off again.

With the inverter plugged in, the car on and a mains cable running from the car to the house the car may be locked and left to its own devices, turning on and off as necessary. In my case on for 10-15 minutes every three to four hours (more often for a standard Prius because of the smaller traction battery) keeping my CH, refrigerator, freezer and a couple of lights running. It will run as long as there is fuel in the tank, probably for weeks in my case.

It is certainly not as economical or efficent as a generator, a Prius costs more, the energy goes from petrol, to 200+Vdc, down to 12Vdc, up to 230Vac, then to the house, with all the conversion losses, but it is there, constantly tested and instantly available and unlike a generator I can use it for other things daily.