From a think tank in Massachusetts to an event space in Manhattan, from a political party in South Africa to news organizations in India and Brazil, investigators tracked hundreds of millions of dollars to groups linked to Mr. Singham that mix progressive advocacy with Chinese government talking points.

Some, like No Cold War, a loose collective run mostly by American and British activists who say the West’s rhetoric against China has distracted from issues like climate change and racial injustice, popped up in recent years. Others, like the American antiwar group Code Pink, have morphed over time. Code Pink once criticized China’s rights record but now defends its internment of the predominantly Muslim Uyghurs, which human rights experts have labeled a crime against humanity.