Nope not a DC coupled battery as the Zappi is just another demand on the home side of the network. The inverter won't know its just for the Zappi. An exception to this is any of the setups that are end to end, ie Solaredge inverter and their car charger setup with their DC coupled battery.
The Zappi can't distinguish between the PV and home storage battery on a DC coupled battery inverter setup. It's purely reliant on seeing export to the grid which most inverter setups do by a few watts in normal operation.
You either provide household demand support via the home storage battery which the Zappi might grab hold of or no household support whilst the Zappi is in operation to prevent it 'stealing' the household side battery.
The international standard under type 2 dictates that the minimum charge point delivery is 1.4kw so the MG will charge at 1.4kw.
If you have an AC coupled battery (arguably less efficient) or use Myenergys home storage battery (so all equipment on their ecosystem) you can prevent the home storage battery being discharged into the car.
The myenergy forum is solid reference point for setting stuff up, used it extensively whilst I was optimising my own setup.