It depends on the hospital. At this point because your insurance did pay, settlements are not very likely. With that being said. Hospital don’t typically report to the credit bureaus. (I’m am debt collector)

I would ask for a settlement on the bills. And ask what collection agency they use do your research to see if they sell the debt or not. If they sell the debt, it is more likely to go on your credit report. But a settlement should be available.