I would try barkeepers friend. Try in an inconspicuous spot first

Steel wool and BKF. Have at it.

@Joseph Corlett, LLC @Ali K Just tried BKF.. no luck :( looks the exact same

bump!

You've got to get more aggressive without cutting through the plating. Put the medium steel wool under a random orbital plam sander please.

There are chrome cleaning products, probably most often intended for cars. I think Brasso is one of them.

Are you sure it's chrome? It looks more like nickel to me. See how it's a different color than the faucet, which does look like chrome?

I do not think that sink is chrome, SS?

My two cents: it is not chrome. I think it is probably "burnished nickel" and the finish is failing. Nothing you can do when the finish fails. Home we bought had cheap "bright brass fixtures" that looked absolutely horrible, similar to your sink because it was the finish on the faucets. I found a good bright brass faucet for one bathroom (still looks good after 20 years) and the other I just had to spray paint with metallic paint.

Try salt& lemon juice.

The sink looks like nickel plating over copper. Maybe it is supposed to look like that if it was marketed as a distressed nickel finish? I see no chrome and no rust.