You said you "just moved," but I assume you moved in 2021, otherwise you wouldn't have a W-2.
You should file as a part-year resident of New Jersey. When you start your federal tax return, in the My Info section, when it asks your state of residence, select New Jersey. Answer Yes to the question asking whether you lived in another state in 2021. Then, for the previous state select "Foreign or U.S. Possession." It's the last choice, all the way at the end of the list of states. Enter the date that you moved to New Jersey.
Later, when you start your New Jersey tax return, one of the first few screens will tell you that it has selected Part-Year Resident as the type of return that you should file.
