Malawian musician Giddes Chalamanda had never dreamed in his 92 years that he might one day be famous enough to dine with the president followed by a night in a luxury hotel.

Last month the singer did both, thanks to his unlikely new stardom on TikTok, a social media platform beloved of youths four generations removed from him — and one he can’t access because he lacks a smartphone or even electricity to charge one...