WASHINGTON — President Biden on Friday nominated R. Nicholas Burns, a veteran Foreign Service officer and a former ambassador to NATO, as ambassador to China and Rahm Emanuel, the former mayor of Chicago and former President Barack Obama’s first chief of staff, as ambassador to Japan. Mr. Biden settled on both nominees months ago, people involved in the process said. But the official announcement was delayed in part because the United States needs the host countries to sign off on such selections before proceeding. The nominations were announced on Friday…