The water heater and stove should work in a power outage. Gas water heaters shouldn't use any electric, and stoves are easily lit with a match or lighter.
I'm assuming any modern gas water heater is in a similar boat, with an electric starter instead of a pilot light - and it's much more difficult/annoying to light a water heater than a stove with a match.
The spark to light the pilot is a piezoelectric thing, manually operated. Newer models (less than ~15 years?) have a control board which is probably mostly mechanical, but does have a flashing LED. I assume that whatever drives the electronics is charged/powered by something that works off the differential of temperature in the chamber vs outside.