To my house.
I came back to follow up -- the breakers were indeed the problem. I found one battery breaker tripped. When resetting it, I accidentally kicked the other breaker off, and then when resetting that, I accidentally kicked the solar breaker off. The end result is a system that works now (charges to 100%, discharges to 0%, discharges to house/car at 10 kW) but gives me strange numbers about steady state house consumption when solar charging is on. Like, my house steady state consumption is about 0.5 kW, and before this monkey business, I'd get that always even with solar charging, but now I see it reporting 0.1-0.2 kW when running off solar. It's like some CT stuff needs calibration.
I did call Solarcity to troubleshoot and they did tell me about checking the breakers.
As for your question, I do in fact see 3.3 kW when charging from the grid, and that's probably 1.65 kW each. I assume there's some configured limit somewhere about how much it pulls off the grid. I don't see the 3.3 kW limitation when charging from solar panels.