John David Washington found himself in a rare situation while promoting his latest film, Netflix’s “The Piano Lesson.” It was his first real press tour in a while, since the rollout for his previous few films (including Christopher Nolan’s “Tenet” and Gareth Edwards’ “The Creator”) were impacted by the Covid pandemic, then the dual WGA and SAG-AFTRA strikes.

“It was a relief to be able to do it like you’re supposed to, as far as getting with the people, right after they see it in the theater, and talking,” Washington says. And after one screening in Paris, his parents — actors Denzel and Pauletta Washington — joined him onstage for the Q&a. “I never thought that I’d be on the same stage with my old man talking about a film that we’re a part of — not in my wildest dreams.”

But, if it was going to happen,...