I'll let the water run but only at a trickle. Enough to get the suds off.

Reason being that to fill the sink with rinse water means that water then has to be drained and replaced after you've rinsed enough dishes that it's gotten soapy or murky itself.

Best option is a faucet with a spray trigger, but in lieu of that, there's ways to do it more responsibly.

Also just a reminder you can adjust the GPM (Gallons per minute) of any faucet with a different regulator. Unscrew the tip of the faucet head, take it to Home Depot or something, and buy one with a lower GPM rate. Kitchen faucets tend to have higher GPM rates, but it may not be necessary for you, so you can reduce it to something less wasteful.