In reality most people will buy "smart" appliances which turn on and off based on price - eg. a water heater which picks the cheapest hour to reheat the tank for the day, or a fridge/freezer which cools everything more in cheap hours, an EV charger which starts selling rather than buying power at the highest priced hours, etc. It's all fairly simple software as soon as energy companies do live pricing, so pretty much every wifi gadget will do it.

People will choose it based on claims in the shop like "Smart timing cuts energy bills by 25% on average!".

It only takes a smallish percentage of demand to be reactive like that and really big price swings won't really happen.

Somewhere they'll still be grandad manually putting the dishwasher on at a cheap hour or turning the hot tub off whenever he sees the price is high, but I expect most to be automatic.