Peak PW output is 7,000 watts or less than 30A at 240V. Keep in mind that is for all loads , so your AC inrush (LRA of compressor and fan) plus all other loads would need to less than that 7kW.
https://www.tesla.com/sites/default.../Powerwall 2_AC_Datasheet_en_northamerica.pdf
Thanks! I guess I'll just try to keep the A/C at ~20A or less so if I'm running the fridge and a few LED lights, it will still be able to start up.