People who buy luxurious second homes in New York City, but live most of the year elsewhere, would have to pay a new tax on the properties under a tentative agreement — an initiative to appease Mayor Zohran Mamdani and liberal voters who launched him into office with chants of “tax the rich.” But the deal, part of a sprawling budget plan announced Thursday by Gov. Kathy Hochul , would stop short of a major priority for the mayor: a broad tax increase on the state's wealthiest residents. The proposed tax on multimillion-dollar second homes, known as pied-à-terres, comes as Democrats are trying to address voter concerns about affordability ahead of this year's midterm elections without alienating the business community. Critics, including prominent business leaders, Republicans, and some moderate Democrats, have warned that slapping new taxes on rich people who maintain apartments and townhouses in New York, but don't consider it their primary home, will just lead the very wealthy to abandon the city.…