Enough to keep the lights on, a fan or charging a phone. Not to run an AC or dishwasher but enough for the basics.
ROI for 24/7 solar+battery is negative in almost all residential cases using current technology and prices.
The difference between off-peak and on-peak rates there is about $0.21/kWh in the summer and $0.29/kWh in the winter, so assume an average delta of $0.25/kWh.
Assuming no solar panels, if you charge the battery on the grid at off-peak rates and discharge it completely at on-peak rates, you break even after using about 3200kWh. Assuming 2 kWh used every day during peak rates that's a breakeven period of 4.38 years.
Maybe my calculations are wrong somewhere, and I'd love to learn if that's the case.
I also acknowledge some big assumptions: namely, that you will always need to use all your stored energy day at the peak time (reasonable in the summer when the AC is running) and that you can use all your battery power for those loads instead of grid power. On the other hand electricity rates tend to go up over time and batteries last for years.
But rates will likely increase. So will the delta between off-peak and on-peak rates. I think the true payback period is between 5 and 8 years.