I'm not sure what the point of this is. Even if Roe v Wade is overruled at the federal level, why does abortion need to be a state constitutional right in New York rather than merely legal by state statute? Barring a tangible good reason, the seems like just Cuomo trying to play up his liberal Bona fides for "some reason".
To ensure that anti-abortion judges can't make it illegal in the state. If it's not in the Constitution, the NYSC could declare that fetuses are persons and entitled to the same rights as post-birth persons and thus make all elective abortions illegal.
I realize that's very far-fetched in New York today, but who knows what the judicial situation will be like years from now?