I don't have smart washers, but I did build a smart ESP32-based [0] zigbee numerical display. Then I use Home Assistant to send the current electricity price to that display when the price changes, and send a notification to all users' phones when electricity is cheap (< 0.05€/kWh) or expensive (> 0.15€/kWh). This helps me plan my laundry and dish washing, which are the only energy intensive appliances I have. I also try to avoid cooking complex meals in the stove+oven.

[0] https://www.aliexpress.com/item/1005010546076391.html

Storing energy in hot water is common is sunny regions, for example Turkey.

Some large cold storage facilities in Germany are trying to optimize electric demand to use cheap peak day electricity. But they have to observe limitations in range of temperatures and capacity of cooling devices.

https://www.cleanenergywire.org/news/cold-storage-facilities...

" Compared to conventional cold storage systems, renewable energy-driven cold storage demonstrates a 10–35 % reduction in energy losses"

https://www.sciencedirect.com/science/article/abs/pii/S23521...

Or plug them into a UPS that charges when it's free but you can run them whenever.

Many of us with solar already do this manually, we run the appliances once the sun is up. Even the hotwater heater is programmed to only heat during the middle of the game.

I've been daydreaming about the tank of water idea as well, but the amount of panels you would need on the roof would be crazy.