Before last season, the guard declined to be vaccinated against the coronavirus, and played in just 29 of 82 regular-season games, missing many because of a New York City mandate requiring the vaccination of all private sector employees in the city that made him ineligible to compete at Barclays Center. But many fans said that his prowess as one of the league’s most talented guards eclipsed his off-the-court controversies: When he played his first home game in March after more than nine months away, the crowd broke a turnout record for a Nets game, and Mr. Irving received the loudest...