For decades, President Vladimir V. Putin turned to one loyal aide for some of his most delicate assignments. When Mr. Putin became prime minister in 1999, he named the aide, Dmitri N. Kozak, his chief of staff. When Russia won the bidding in 2007 to host the Winter Olympics seven years later, Mr. Kozak managed the preparations for the Games. When Mr. Putin annexed Crimea in 2014, Mr. Kozak oversaw its integration into Russia. As Mr. Putin massed troops in 2021, Mr. Kozak was telling American diplomats about the evils of the Ukrainian government. These days, Mr. Kozak, 66, is not responsible for much at all, with many of his powers having shifted to another top aide, Sergei V. Kiriyenko, according to three people close to the Kremlin, a Western contact of Mr. Kozak and a U.S. official. Mr. Kozak has disappointed Mr. Putin, they say, because Mr. Kozak has made it clear that he believes the invasion of Ukraine was a mistake.