Just a quick check of the official website to try and get onto Medicaid in WA state shows that it requires a social security number and citizenship information: https://www.wahealthplanfinder.org/us/en/health-coverage/get...
Some states even allow legal temporary visa visitors like students to sign up for their state level funded medicaid. NY is constitutionally required to do so.
ICE however is making a play to obtain all of that state level data.