You need to break your lease on or before June 30.
If you break your lease (or it ends normally) on or before June 30, then you are a part-year resident of VA from January until the day you move into your parents, and you are a part-year resident of New York starting on the day you move in with your parents. Your domicile, for tax purposes, is determined partly by your intent, and if your intent is to leave Virginia permanently and live in New York, that will determine the day you change your domicile. This is a normal tax situation and Turbotax handles this easily. VA will tax you for income earned while you lived in VA, and NY will tax you for income you earned while living in NY. (Other income like interest, dividends, and so on, are taxed based on where you were living on the date they were paid.)
However, even if you change your domicile, VA will tax you if you maintain an abode in Virginia for 183 or more days, even if you don't use it. (There is a technical definition of abode but we don't need to go into it, since an apartment clearly qualifies.) If you have a Virginia abode on July 1, 2024, Virginia may want to tax you for the whole year.
