Honestly, I feel like many hospitals run that way. like if there is no specific residency application then just apply to any regular listing of a unit and then they'll find out you're a new grad and place you into the residency automatically! It doesn't hurt to try!
I def think there is an advantage of being in state or being an internal applicant/someone who studied in NYC. LIke I am from NJ and they straight up said to reach out after I am done graduating.. but tbh I am losing patience with it and don't want to lose any other potential offers that I may get. So currently I have also applied to jobs in NJ and also applied to get my NJ nursing license first because I have heard from other nurses that new york can take months to get around to licenses for people