I have gotten white haze off of pans by wiping with vinegar. I would ask Kohler in that it is an acid. They will likely say no to anything that is not on their 'list' though.

'The other side where the drainer sits and that doesn't get much water looks like new. '

This sounds like it could be mineral deposits. Food grade vinegar does take that off. Long term use is the question. Is this cast iron black enamel or a ceramic bowl?

It is black enameled cast iron. I've tried vinegar but I didn't leave it on very long. I agree that it is mineral deposits.

I've also used Method All Purpose to remove mineral deposits on faucet areas, letting it sit. It has worked as well as the vinegar. I would think it's more gentle to finishes.

Yes I tried the Kohler cleaner. I think I have some Method cleaner I could try. This morning I tried some old Shaklee Basic H I had but used it full strength. It did improve the situation. I don't understand all the restrictions on what to use. I would think this type of surface should be more resilient than the cleaning options they give. Maybe not things you would use every day but for once in a while when the weakling cleaners aren't cutting it.

The Method spray did a good job and smelled nice (lime and sea salt)but again more of a daily cleaner once I get the dried on deposits off.

Letting them soak in vinegar or lemon juice should remove the stubborn deposits. It has to sit.

I have used CLR to dissolve hard water deposits. It is a powerful chelating agent and I wouldn't leave it on too long. Again, ask Kohler.

I clean mine with Barkeeper’s Friend, dry thoroughly, then using a paper towel generously apply mineral oil and wipe dry. This lasts maybe a couple of weeks.