Fun fact, a generater should be relatively simple to make if you have a design handy, it’s not even all that hard, just very time consuming.
You’re going to have very poor efficiency, but I don’t think economising on fuel is going to be that big a deal, basically you just need a big axle, a big casing, some really huge magnets, and a crapton of wire. Portable generators should be totally fine, as would “permanent” larger generators.
I agree that existing building walls should just be assumed to have power plugs everywhere, also we’d differentiate a “shelter wall” that’s just a wall from a “house wall” or similar, that would include electrical hardware in the component cost, so you could build your own house out in the woods or something, and a recipe to retrofit cabling into an existing wall.
Appliances would check for an adjacent wall, then search around on the map for a connected generator or batteries, and pull power from that. I’m not too concerned about the precise mechanics, it’s not too hard.
The main thing holding it up is infrastrure-ish stuff, we need our framework that tracks activities that happen when the player isn’t around.