I don’t know where the 800W is coming from. It is quite common to have 16A breakers on a circuit. That is 3,8kW. My regular apartment has 3x20A breakers and for example my induction hob is 7,2kW two phase.
If you add the battery to a 16A circuit then you can theoretically draw 3,8kW + 800watt on it with the battery.
With this Pila battery you could put 3,8kW + 2,4kW on the same circuit!
If you want more than 800watt you can't use a regular plug in your house, it has to be a dedicated circuit.