That being said with ESS, any load on the output of the inverter has to be smaller than the inverting ability of the inverter or if grid connected smaller than the passthrough ability of the inverter.
The ideal set up is grid into the input - loads on the output with the exception of the use of an energy meter which allows some energy to be injected backwards.
With ESS you can export excess solar and sometimes battery to loads before the inverter (ac input) if there is a grid meter that communicates with the GX for the inverter at the grid or incoming side.
Since you also have this is would need a way to know about it as well.