Over the past two years, an unlikely superstar has re-entered the zeitgeist in a major way: Fred Rogers. The gentle television host died in 2003, leaving behind more than three decades of cardigans and aphorisms. His show, “Mister Rogers’ Neighborhood,” lived on in PBS reruns and a popular spinoff (“Daniel Tiger’s Neighborhood”), but Rogers was largely a relic from an era when children weren’t born with smartphones attached to their umbilical cords.