NEW YORK — The president of the New School in Manhattan is about to lose an extraordinary perk: a five-story West Village town house that for decades has served as the university head’s official residence. The school, which projected a $52 million budget shortfall for the 2024 fiscal year, is asking $20 million for the home as it seeks to stabilize its finances. The sale comes as shaky student enrollment, inflation and other forces are threatening smaller colleges in New York City and around the