New York state lawmakers have approved a tax on multimillion-dollar second homes in New York City. The measure, backed by Gov. Kathy Hochul and Mayor Zohran Mamdani, targets properties worth more than $5 million owned by people who do not live there full time. It passed as part of the delayed state budget on May 28. And it marks a rare point of alignment between the progressive mayor and the more moderate governor. The so-called pied-à-terre tax is projected to generate $500 million a year. Officials say the money will help close a $5.4 billion city budget gap without a broad property-tax increase on regular homeowners. But independent analyses suggest the actual haul could fall short. Critics warn it may trigger an exodus of wealthy owners and reduce other city revenues. The debate reveals deep tensions over how New York funds its services and whether it can afford to alienate high-net-worth residents. Hochul and Mamdani announced the plan in mid-April.…