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This has been done for close to a century in wind or run of river hydro heavy countries (as well as some coal ones).
The water heater has a buffer tank and is attached to a meter that only runs when a signal is sent across the power line. This stores about 20kWh for a 300L tank.
Modern insulation would allow going up to a few m^3 for a couple weeks’ worth.
Combine that with some radiant floor heating on a nice thick concrete slab and you could use the battery for home heating. (Though it would need a lot of water.)