One of the first calls Obama made after U.S. forces killed Osama bin Laden in 2011 was to George W. Bush to spread the word that the mission had been accomplished, said Kate Andersen Brower, author of “Team of Five: The Presidents Club in the Age of Trump.”

At a pomp-filled state funeral, mourners paid tribute to Mr. Carter and argued that he was a more successful leader than many remember. “It’s time to redeem his presidency,” a former aide said.