President Donald Trump nominated a senior State Department official Thursday for the top post at the U.S. Agency for Global Media after a federal judge ruled that Kari Lake's leadership violated federal law. Trump nominated Sarah Rogers, the undersecretary of state for public diplomacy, less than a week after U.S. District Judge Royce Lamberth ordered that all actions Lake took as acting CEO from July 31 to Nov. 19 be considered void, including an Aug. 29 reduction-in-force that eliminated jobs for more than 500 employees at Voice of America and elsewhere within USAGM. Lake insulted Lamberth's appearance Thursday as she criticized his ruling last weekend. She said on X that she would stay on as deputy CEO and that Michael Rigas, who is deputy secretary of state for management and “a patriotic fighter with experience reducing the size of government,” will be acting CEO.…