I had 2 primary residences in 2021. I moved to NYC on 10/19 and worked in NYC at Starbucks from 10/29-11/16. Am I exempt from New York income tax liability for 2021?

I am wondering because this fall I became a full time student (under 25 yrs old) so I don't know if I should submit my W-4 as exempt from New York income tax liability.