V2G won't be using the car's inverter.
It will need to be an approved inverter designed and approved for grid connection. Early models will be expensive but frankly it shouldn't cost a lot more than a regular hybrid grid-tied inverter which uses 400 V battery architecture and can talk with the car battery's BMS (the same as it would with a regular home battery, or DC charge stations do now).
We will see more integrated solutions with solar PV and home battery, along the lines of what Sigenergy have with their DC charger. That's capable of bidirectional but not approved as yet for reverse flow.