Soft scrub and a scrubby
Bon Ami or Bar Keepers Friend.
MR CLEAN MAGIC ERASER OR OXI CLEAN POWERED DETERGENT (SCRUB)
Barkeepers friend. It’s helpful on white dishes too.
I use Bio Clean paste. Works on so many things. It is super fine paste that removes stains.
When I had a porcelain sink, I would occasionally fill the sink with water and add a cup of bleach and let it sit for awhile to do it's work. That not only sanitized the sink but it also removed the marks from pots and pans. An option once the marks are removed would be to add a sink mat so that the pots & pans would hit the porcelain anymore. Of course, you'll need to remember to clean the underside of that mat on a regular basis.