[axiolite]

> there isn't a remotely affordable consumer friendly solution for "I want these batteries to take over when my power goes out".

That's called a UPS. You can buy them in stores. Closer fit for this purpose might be solar-charging portable power stations, which are also COTS hardware that similarly costs a few hundred dollars each.

Anything more elaborate than that needs to be wired into your breaker box, requiring licensed electricians and inspections. Not terribly expensive, though. Installing an automatic transfer switch in your home is pretty common in rural areas with frequent power outages, for generator installations.