@Joseph Corlett, LLC replaces double bowl sinks with single bowls on a regular basis without replacing the counter (he enlarges the cutout.) He is a frequent contributor to the Kitchens forum so I tagged him for additional advice.

You can definitely replace the sink, with a bigger one even, but you need to find the right company in your area.

That doesn't look like corrosion to me; stainless steel doesn't easily corrode or rust. It looks like a consistent abrasion with some black contamination, which is usually from a leaking sink.

We would drop those sinks, refinish the stainless steel to new, and strap the sinks back in place. There would be no more leaking, corrosion, or contamination. Expect to pay $750.00 - $1,500.00. Cutting a new cutout, profiling, polishing, and undermounting a new sink would be in the $3,500.00 budget range, sink and plumbing included.

Joseph, thank you for your observation that it didn’t look like corrosion. After scrubbing it with a stiff brush and some 409, it seems it was just excess clear caulking, which is what make it look lumpy and damaged. Once it loosened a bit I was able to scrape it off with a fingernail. Now to go around the rest of the perimeter.

I’m glad I asked. You just saved me some angst.

I’m wondering if the caulking was added more recently to address a leak or something?

Not sure how to determine if that is the case.

Undermounted sinks can't be successfully topically caulked, because the caulk that's working as a gasket is between the sink flange and the bottom of the stone. That's why undermounted sinks must be dropped, the stone and sink flanged cleaned, the sink re-caulked and strapped in place.