Your spending more energy engineering that instead of just buying a tankless water heater if you care that much about it.
More and more “tank” water heaters are moving to heat pumps which should use less electricity overall than a tankless (if you can handle the possibility of running out of hot water).
Which full circle going back to the original discussion of turning off the heater. You probably end up close to no/low savings. I can see an argument of a smart heater being able to slightly adjust load at peak times but I engineering a heater to turn off when you are sleeping and then heating back up before use is probably going to not have much savings. Those heaters are increasingly made to edge out at maintaining the heat and take quite a few hours to heat up.
They are crap. 8kW is typical, and the pressure for a reasonable water temperature is low.
I haven't knowingly used a more powerful one. I suspect that would negate the cheap installation cost, as it would need a three phase circuit.
https://www.homedepot.com/p/Rheem-Performance-36-kw-Self-Mod...