Life outside the White House has been sweet for former President Barack Obama, with perhaps the most difficult thing being the one he does best: politics. Mr. Obama is navigating a landscape in which he must fit his obvious relish for the celebrity lifestyle with an unwritten code of conduct for past chief executives, a world that is his for the taking yet tradition dictates he do so incrementally. It’s a political scene where players may covet his endorsement or desire his invisibility. Mr. Obama enjoys tremendous post-presidential popularity within the Democratic Party’s rank and file, but he has not...