I will say that just because you have medicaid, doesn't mean that you will be deemed a public charge. A lot of factors are weighed when that assessment comes. I would look into if the medicaid option is state or federally funded.

Here's something from the NY state of health site.

"In New York, most immigrants are enrolled in the Essential Plan and are not impacted
by the Public Charge test. Of the limited number of immigrants who have Medicaid,
most are enrolled in Medicaid that is fully funded by the State, not the federal
government. This coverage is also not included as a factor under the new rule."

https://info.nystateofhealth.ny.gov/...%20NYSOH_0.pdf