WASHINGTON—A “Real Housewives of Beverly Hills” TV star, a Paralympic swimmer and a self-described “brand king” were among the Instagram and TikTok influencers who were paid by Chinese officials for a discreet campaign that promoted the Beijing Winter Olympics, new Justice Department documents reveal. The social-media posts fanned across a variety of popular Instagram and TikTok accounts that have a combined following of 5 million people who follow their videos, photos and content about travel destinations, sports, fashion and women’s issues. The Chinese Consulate in New York paid $300,000 to New Jersey-based firm Vippi Media to recruit the influencers. The...