>> That the Powers of Government may be reassumed by the People, whensoever it shall become necessary to their Happiness; <<
Did that mean?
1. There should be a lawful means by which the People should be able to win redress for their grievances, amend the Constitution as they see fit, and even, hold a Constitutional convention so as to replace the Constitution as a whole when the entire People concur that the new government is failing at its aims of securing freedom
or
2. If anyone subgroup of the People feel so motivated, they can declare that the Laws of the government do not apply to them any longer?
Notice there is no portion of that quote which makes any mention of the State taking action separate from the Nation.
Does the clause reserve the sovereignty of the State of New York, or the People of the State of New York?
I presume it meant the people of the state or the people of the state acting through special conventions, such as a ratification convention like themselves or a secession convention. Various seceding states in 1861 put the question of secession directly to the voters of their states. That did not occur during the ratifications of the Constitution, so the secessions of those particular states would seem to have more legitimacy as an act of the people than the ratifications of the Constitution.
The Tenth Amendment says "The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people." The state ratifying conventions that said they could reassume their governance or proposed wording like the Tenth Amendment in their ratification documents were a majority of the states ratifying the Constitution. And, of course, three quarters of the states ratified the Tenth Amendment making it part of the Constitution.