Call a very large fabricator that offers service. Tell them you need the sink secured....that's it's fallen some. Ask for a Hercules harness....or you can provide one if they don't offer. Look on Amazon. Or try to find out who the fabricator was for this install. Looks like possibly late 90s to 2000s install. Expect to pay $200-$500 for a service call from a fabricator....depends on travel time and other variables.

Arik:

We do this call regularly. Believe it or not you're very lucky because your problem is obvious. It's the sinks that leak, oxidize reinforcement rods, and split the stone without showing themselvs that are unfortunate.

If you see any black/brown recurring crud at an undermount sink, that sink is leaking and unsanitary. No, topical caulk won't fix it. The sink must be dropped, the flange and stone bottom cleaned, and the sink strapped in place with a Hercules Universal Sink Harness or a Sink Strap or two. With the placement of your drains, I'd recommend the HUSH for your repair. No blocking, no clips, no bridging the flange with stone scraps and polyester please.

I'd change it to a deeper single bowl were I you. Nearly the same amount of work.

"Call a very large fabricator that offers service."

He'd have to be a licensed plumber were he in Florida.