I bought lights-out manageable 400 lbs (lots of kWh) of rack mounted sealed lead acid batteries in the form of UPSes with expansions for less than $600.
The other thing is that rewiring a main panel for generator and/or solar to provide emergency power to a subset of circuits is preferred to simply trying to power everything with a tiny battery pack. This usually means adding a subpanel and an automatic transfer switch, which is a heck of a lot simpler than running extension cords through the house and much more fine-grained than powering everything with backfeed.
The other thing is that rewiring a main panel for generator and/or solar to provide emergency power to a subset of circuits is preferred to simply trying to power everything with a tiny battery pack. This usually means adding a subpanel and an automatic transfer switch, which is a heck of a lot simpler than running extension cords through the house and much more fine-grained than powering everything with backfeed.