ALBANY – Politicos across the Empire State are mourning the death of legendary power broker Sid Davidoff, who spent decades ironing out deals for some of New York’s most influential leaders. He was 86. Davidoff, the aide to ex-Mayor John Lindsay, died early Sunday at a hospital in the Dominican Republic surrounded by his family, Linda Stasi, his widow, told The Post. “He was just a true New York character,” Stasi said, describing the lobbyist as a proud “Jewish tough guy.” The label might be