I had a black silgranit sink years ago and loved it for the most part, except when the water wouldn't completely drain like yours. I found that if I used some mineral oil (baby oil) and a microfiber cloth, it would polish it nicely and repel the water for a few months. Definitely apply it to the microfiber cloth and polish away, then let it sit as long as you can (I found overnight to be best) and you should hopefully be good for a while.

SPOT TEST AN INCONSPICUOUS AREA FIRST!!!!!

That ring looks like plumber's putty bleed or something. It may be possible to poultice it out and reinstall the flange with silicone. Spraying the sink with Magic Countertop or similar would probably aid evacuation.

Thanks Lynn and Joseph! I will try both - I’ve used mineral oil on previous sinks and it works well.