Since you can't find nothing, 3D-print a holder, add actuator (worm shaft on reversed squeeze flush bottle or something), sensor, solar cell and capacitor?
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I actually just found this and I'm considering if I should actually just go for it.
https://www.instructables.com/3D-Printed-Automated-Liquid-Dispenser/
Maybe look at commercial soap dispensers? Commercial products are almost always repairable and readily available. Anything electronic usually isn't BIFL though, at least not anymore.
I tried but can't find anything available to buy and anything I find is wall mounted giant units.
Websearch for 'squeeze flush bottle'
They are one handed and supposedly non drip.

That's kinda what I have already. I wanted a zero handed option so I dont even need to take my hand off the brush.
Understood.
I've never used an automatic one.
A bar of soap?
For doing dishes? never seen that around here. Also regardless of that I have extremely hard water so almost any bar of soap does not work nicely at all since it instantly leaves a lot of mineral deposits. Only bar of soap I know that works is Dove cream bar but that is just for hands and body use, not for dishes.
That has actually been picking up steam on social media if I remember.
The idea is that you have a bar of soap + a harder bristled brush (IKEA sells cheap ones but there are probably BIFL ones) and then you just froth up some soap on the brush with one hand and then use it to scrub the dishes.
I think those people used special soap formulations though that weren't just a dove bar
I can imagine it work, but as you say it should probably be a special soap formulation, especially if you have hard water. I Once tried bar soap shampoo that was "recommended for hard water" and it was still a disaster and my hair was like a stiff bristle afterwards due to the mineral deposits.
Ah, if you’re doing dishes I have another tip. Fill a vessel with ca 5 liters of hand warm water. Add a teaspoon of detergent/soap. Rinse your plates. That way, save water and detergent. Never do your dishes with running water, bad for the climate.
It might waste fresh water, but that's not climate.
Besides all the fresh water wasted by everyone in your local city is a fraction of the water wasted by nearby industry and farming. Your individual "Environmental Footprint", is a concept invented by the fossil fuel industry to shift the blame (and responsibility) away from them.
Improve the world, start with yourself :-) Sure, all of us must vote for the right party to save the climate. However, you are using hot water to do the dishes, right? And detergent is made and transported with the help of fossil fuels too. Now think how many households there are in your village, your town, your country; it’s massive. And, as you do the dishes, you can think about ways how you can protest against Big Industry - killing two birds with one stone, if you pardon the expression.
Starting with yourself doesn't have any effect on the world. It only effects your life. So if that's your goal, great! But don't pretend saving a few gallons of water a year matters to the world. The world is huge. Your village is tiny. You have to think bigger if you want to make a difference.
It's both sides. The industry ultimately just serves end customers and putting it all on them is just an attempt to shift the responsibility away from users. If people weren't buying all the meat, cars, electronics etc. the industry would disappear.
What problem has ever been solved by blaming, shaming and asking everyone to willingly give up something?
Nothing. That's not how people work. They just start to dislike you, and fight you.