Our sink has cracks in it.
You can buy a kit from you hardware store, but I have seen reviews in this group where people have tried them with little success.
I wish that there was a way. My kitchen sink, 12 years old, looks like it has been through a bombing!! I read, researched, seems nothing works. I have beautiful granite and don’t want to lose that, but the stupid sink is an odd shape, so I cannot find another like it.
My marble sink did that as well but everything else was still perfect. I bought some spray paint from Home Depot (tell them what you are using it for and they will direct you to the correct type of paint). I taped off the top edge of the sink where I wanted the paint to stop (it was a slight different color as my counter is off white and this was white but it looks good). Start with a light coat and then let dry and continue light coats until desired coverage. Mine has held up for years now. This way one can make the sink different colors for a different look if one chooses to do so. My marble counter top is a light grey and off white marble so next time I may do a light to medium grey, just for a different and pretty look. Make sure you cover up everything around this within at least 2 feet for the over spray.
Forgot to mention, you might also want to spray a clear coat on it for longer lasting.
Rustoleum has a kit that works very good u need to mix it well but does the job i used on 2 shower stall floors that were marble and homeowner messed it up by using wrong chemicals to clean so used this kit came out good
IF the sink is part of the entire countertop and not separate, it is faux marble. These were popular in the 80s. I have one in my bathroom and the "crazing" looked just like yours. I have looked at ways to repair it and came up with sanding the surface with a 4" power sander and finer sandpaper disks so as not to leave gouges in the plastic. Some of these sinks are solid surface and the color goes all the way thru. Some are not. Only sanding will reveal it. Once sanded, it will need to be polished. Jeweller's Rouge can do the job but you will need a felt pad on the power sander to polish the inside of the bowl. Automotive stores sell the rouge as does Amazon. I recommend removing the chrome drain while doing this. Just unscrews from the bottom and pulls out from the top. You'll need some new plumber's putty to re-install the drain.