The first time Robert Draper heard about the psychedelic drug ibogaine, it was from an unlikely source: the retired U.S. senator Kyrsten Sinema. As a political reporter for The New York Times, Draper often talks to figures like Ms. Sinema. But on this occasion, he said, she wanted to tell him about how she had tried ibogaine, which is illegal in the United States. She’d become such a believer in…