An average faucet flows at 2 gallons per minute. An average dishwasher uses 4 gallons of water. Unless you can do your dishes in 2 minutes, dishwasher uses less water.
You leave your water running while you wash your dishes?!
Having lived off-grid without running water, I know very precisely that I use slightly more than a gallon of water to hand wash my dishes. No way a dishwasher beats that.
It's a moot point anyway. I don't have a dishwasher and I'm certainly not going to remodel my kitchen to make room for one.
Ref https://www.cnet.com/how-to/how-much-water-do-dishwashers-us...