The solar technology commonly being sold in California apparently isn’t ready for prime time.
I would think just switching off the main breaker should run the lights and refrigerator in the daytime.
You should be able to just plug an inverter/battery system into a standard socket and charge it up during the day to run the lights at night.
Household devices might be given plug-in priority boxes, so the electric water heater doesn’t run when the refrigerator is drawing power.
Priorities might be in the order: plug-in lamps, stove top, oven, refrigerator, air conditioning/heating, battery backup and water heater.
Probably a reg against that.
an off grid input Transfer Switch should be installed when you put in your system