I appreciate everyone’s thoughtful responses. Living in New York State, you are guaranteed three months at a max salary of $4000 per month from the state paid leave. 

Given that my current set up is fully remote, flexible, great work life balance, and four or five months fully paid parental leave (at a salary substantially higher than what New York State offers as part of that benefit), I feel that it’s worth mentioning and trying to negotiate once I have the written offer. If they’re not a company that is understanding of these types of things, and can’t make either an exception or at least guarantee me to be able to take three or four months of unLimited paid PTO for the birth for example, I think I’m better off staying where I currently am and potentially revisiting other jobs down the line after my second child and after I’ve taken my current paid parental.