This seems like an opportunity for all that currently-useless "smart home" tech that companies are so eager to sell. I don't need smartphone notifications from my internet connected washing machine to tell me when the laundry is done, because i know when i started it. But if i could load the washing machine and tell it to switch on when the cost of electricity dropped below a certain threshold, and it would actually save me money, then suddenly the smart home would actually be providing some value.
unfortunately, as far as i know not only is there no consumer tech that does this, but energy companies don't make real-time pricing available to all but the largest consumers.
At least for the specific case of washing you can get most of the benefit by moving to a time-of-use tariff and scheduling the washing machine to run during the off peak time.
(Washing machines do seem to use a surprisingly large amount of energy, particularly the ones that heat the water internally).
With a quick search I can't find any energy company in my area offering time-of-use tariffs. I remember in the 90s it used to be standard to have a cheaper night tariff. But there's nothing that actually does impedance matching through financial incentives.
By the second spot rates might be slightly too volatile for the average consumer to use, but what you could have is smart pricing mechanisms where you can e.g. lock in a rate for the next 1 or 2h and then your washing machine waits for the expected best rate in the day and with maybe a timeout when it starts anyway (if you need it).
That way you could usually get good rates when you start your washing machine in the morning and it waits a few hours, depending on price history.
This is just a case of simple enough statistics that they can be calculated on the smalles microcontrollers available. Those are already in most home appliances. If you now add Wifi capabilities (which also a lot of home appliances have), you could get the communication done.
For any smart appliance the marginal cost to implement this is zero. The investment cost is only the software.
unfortunately, as far as i know not only is there no consumer tech that does this, but energy companies don't make real-time pricing available to all but the largest consumers.