NEW YORK — The Rev. Al Sharpton had never seen anything quite like it at his Harlem headquarters. Adrienne Adams, who became the city’s first Black City Council speaker in January, had just finished an emotional speech on Martin Luther King Jr. Day when she took half a beat. Scanning the room, she slowly pounded her right fist into her left hand, and said, “I leave you with this.” Then, in what she later described as an unplanned flourish, she began to sing, surprising the crowd at the National Action Network with a soaring rendition of “I Want Jesus to Walk With Me,” an African American spiri…