Regarding human/animal power
Similar to @Loewian by a regular valve the human is actually relieving the pressure that is in the pipe (so the first water that comes out is regarded as human propelled ( source))
But by an electrical valve the human is not reliving the pressure physically but it is only being caused by him
(There might be an opinion that if a robot washed your hands it is OK, then it will be OK in our case (b"n I will look for it))
edit
I might be wrong since the human is the one activating the valve, (by the monkey the monkey is pouring not because of the human but by himself)
Edit I think I am wrong
There is a biblical requirement to shecht an animal to eat it, there it is clear that you need the shochet's propulsion,
but if the shochet propelled something (a stone) and that thing (the stone) propelled the knife is not written clearly if it is sufficient
but to the simla chadosho 3.2 decided that it is not sufficient since it might not be considered the shochet's power
In our case the washing of the hands is a Rabbinic decree so it is very possible that the koach kocho is considered his koach (that propelling something by propelling another thing is considered his propelling)
So causing the valve to open by triggering the electric motion sensor which then triggers the electric valve might still be considered human propelled (I do not see a reason by extra steps in process sill be different then just 2 (ie hitting the valve by throwing a rock on it)
Would waving your hand to turn on the sink still be considered koach gavra?
it might so if no choice you should do it, but still cover your hands