After some rather unsuccessful attempts at reusing some large lead-acid batteries I got for cheap (which were not fully broken when I got them, but I managed to break them in the process), I caved in and bought a 5.2kW LiFePO4 battery pack (was 25% off at a local store).
Still needs some more hooking up, and due to some stupid regulatory reason I can't install solar panels yet, but I hope to already use it as a backup power supply over the winter.
The hybrid inverter is quite cool as it allows hooking up two individual strands of PV and also export a lot of very detailed data to the open-source Home Assistant software. Also seems to have a built in UPS feature for connecting servers, but I need to test that first (by default the emergency backup power only kicks in after a few seconds).
So, not really offgrid living, but the system would allow an off-grid setup at least.
5.2 kWh? kW means nothing for a battery.