Can the "silver cleaning trick" be done in a stainless steel sink?

Try this method. https://www.hometalk.com/diy/clean/house/how-to-clean-stainless-steel-sinks-and-make-them-shine-2534786

If you’re referring to the “foil, baking soda trick“, yes, it can. I’ve done it in my stainless steel sink with no problems.

For cleaning my silverplate (not solid silver), I find I still prefer a proper cleaner intended for silver as I didn’t like the look of my silverplate after trying the foil/baking soda method. If I’m in a hurry and have just small items like a silver bracelet or a serving spoon, I use regular (not gel) toothpaste.

I always wipe my SS sink with undiluted bleach, wait a minute and rinse. In the past I also filled our double walled coffee mugs with hot water and asplash of bleach, soak a couple of minutes and the dirt floated off. Now I use Oxyclean on all cups/ mugs to remove stains.

Yes you can....BUT

I sell a lot of silver on Ebay. Jewelry, silverware, serving sets. Silver polish and dips tend to remove some of the metal. The foil method doesn't work that great and still leaves a grey film that still needs to be removed. I use white toothpaste (not gel)and a damp toothbrush. For large items I use a damp cloth. Also works on copper, brass, gold, porcelain, ceramics, sneakers, plastics, etc. For my sales I needed one product for cleaning everything.

For a stainless steel sink, the easiest solution to clean is Bar Keepers Friend that can be found where Ajax and Comet are sold. It is great!