A larger than 1 kW inverter will have more ability to deal with startup loads. But the sustained, steady state capacity of my 2003 and 2010 Prius were only: 1 kW ~= 75 A * 13.5 V - steady state Higher currents would drag the voltage down keeping the power output at 1 kW. Below 12.85 V would start discharging the 12 V battery .... not a good thing. Bob Wilson ps. I no longer have Prius and just recently had an inverter returned.
I believe that recommendation was for aftermarket inverters powered from the 12V system. But I understand the OEM 120V-outlet inverters in the Primes (Prius and RAV4) run from the traction battery, not the 12V, so are not constrained to the same limits.
Yes, the PHEV's outlet comes from the vehicle charger assembly, so the inverter inside that assembly is drawing from the traction battery. The Japanese HEV's outlet I don't know - it has a standalone inverter, but I've not found the circuit diagram to tell whether it connects to the high or low voltage system. But it is specced at the same 1500W.
The 120v outlet on my 2024 Prime SE is pretty robust - I just finished washing the car with a 13 amp Pressure Washer plugged into it. No problem with multiple starts and very convenient!