I hope the next step for this is plug-in battery storage. All the on-grid battery hybrid inverters I can find in the USA are either single leg 120V or 12kW for $5k. I just want like 3kW dual-leg with support for a dozen kWh of batteries

Yeah it seems like the inverter manufacturers don't see demand for that. I was thinking maybe the Victron Multiplus-II 2x120 could be paired for 240V output but I was wrong, that's only on grid power, it won't make 240V from battery.

Obviously the inverters and pairing technology exist, but I don't know where to buy one retail.

Victron devices on sale in Europe/UK all do 240V output. I've seen someone do a boat build in the USA with Victron hardware that included 240V circuits (because the builder was a UK/US person, and they wanted both 120 and 240 "normal" circuits).

Yeah you can use a Victron 230V inverter along with an Autotransformer to get split phase 240V. Also, I was sort-of mistaken in my earlier comment but can no longer edit it. The MultiPlus II 2x120 cannot make split phase 240V on battery, but I see that the regular MultiPlus II can be paired to do exactly that. About $2K for a setup capable of 240V 20A. Not inexpensive, but it is Victron, which is amongst the best.

I've seen setups where they put a 48v battery between the solar panels and plug-in micro inverter. No idea how this impacts efficiency or if there's any safety concerns though.

this exists and ikea sells them

welcome to the future

https://shop.sveasolar.de/category/ikea-shop

The Bluetti Apex 300 is an expandable 2.7kWh 3.8kW dual-leg battery + inverter + solar generator for ~$1000 (on sale).

The EG4 12kPV does 8kw split phase output and is $3k, but haven't seen anything smaller than that yet.