Borax! I promise. I put it in one of those plastic ketchup/mustard picnic bottles with the spout. I cut the end to make the whole a little larger. Wet the sink and “spray” some borax all around it. Let it sit a few minutes if it’s really bad but then just scrub with a microfiber or scrubby sponge. Sparkling clean! This works great for stainless pots and pans too.
As a reference, I am familiar with Barkeepers Friend (and have it too) but the Borax is even better for steel and definitely not as hard on your hands, etc.
Edit to add: I wouldn’t use the Borax or the Barkeepers Friend on the fridge or stove as those are coated or polished - it’s different than sinks. The trick to the stainless appliances (and steel actually) is always polishing with “the grain”. We use microfiber cloths and a vinegar and water spray to clean, scrubbing in the direction of the grain. If you want to shine it up, you can use just a tiny tiny bit of olive oil on a soft cloth and rub it with the grain.