Interesting idea, however impractical because of under floor heating, if you are going to recover heat from waste water then you need to look at doing whole system not just the shower.
The dishwasher and washing machine use far more water and it's warmer to start with, but the whole problem is recovering heat without causing a maintenance problem, and to restrict to flow to allow heat transfer will mean it will get blocked with female hair.
I looked at the same problem with the tumble drier, my thought was why suck the pre-heated air from the room, heat it more, then put it outside before removing the heat? We have heat recovery units why not recover that heat?
However it is simple, running cost for tumble drier pre-year £75 so maximum that can be saved is less than £75 as in summer you don't want to recover the heat, so around the half mark so £38 any unit would be redundant if a non vented model is used, so you simply can't build one cheap enough to be worth using.
With an electric shower they are rather poor to start with, so pre-heating water could help get more than a spray of hot water, but this would need to cost less than using gas, and using gas to heat water then no real need to pre-heat the water.
There is a name for the devices designed to save which in real terms don't it called "snake oil" and that's where yours seems to fit.
I would not call your idea "snake oil" but I would say its a complete waste of time and money because the footprint is too small for it to work and by the time the water has left the shower head and touches the floor it will have lost most of its heat, so making your idea a waste of time.
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