If you're concerned about emergencies: for $38 you get a self-contained LED camping lantern that lasts for 30 days on a single charge [1] at the lowest brightness, or 2 days (off at night) on full brightness. For a tiny fraction of the price of a Tesla-based emergency power solution, you could buy two of those for every room, plus an RV cooking gas burner and a big propane tank that covers heating, making food and hot water for washing. Hell, even a big diesel generator would be cheaper (not to mention it's readily available).
The main thing I'd really like to be able to backup is my (oil) furnace in the winter so that it could continue to operate in a power outage. Though,truth be told, I could get a bigger propane tank and either run some backup heat off that or a generator for a couple of my circuits.
Pretty much everything else can go out. Obviously food could spoil in an extended outage, but that's a fairly modest cost in the grand scheme of things.
How about installing a wood-burning fireplace? Super cozy also in daily life, probably adds to the resale value of your house, and you can keep firewood indefinitely as long as it's dry.
As for food: stock canned goods for a week. (There's a reason preppers have rooms full of the stuff.) You probably also want to stock bottled water for a week, just in case.
I have both a wood stove and a wood burning fireplace. The backup was part of my justification for getting the stove. I don't know if it would be sufficient if I lost power for an extended period of time in really cold weather to keep pipes from freezing but you can't guard against every eventuality. (I also worry about what can happen when I'm not around.)
As for the food, I'm close enough to civilization that I'm not too worried. Worst case I get snowed in for a couple of days. I won't starve.
[1] https://www.amazon.com/Ultimate-Survival-Technologies-30-Day...