It would be a mistake to see Kubrick's black and white 1964 classic as outdated and irrelevant. I just watched this following the Russian invasion of Ukraine and the release of a telephone conversation between Trump and John Daly in which Trump brags about telling his "friend" Putin that if he invaded Ukraine "we're hitting Moscow".
With that in mind, it makes this fascinating documentary as timely now as when the movie and documentary came out. It's a balanced mix of movie clips, interviews, old animation, and frightening video of actual atomic bomb explosions.
Trivia not covered by the documentary: Kubrick tricked George C. Scott into doing some over the top "practice" scenes for comic effect. Scott agreed, but didn't want that approach in the film and refused to do it that way during the actual filming. But Kubrick secretly recorded Scott's practice scenes and included them in the movie.
Scott was furious and vowed that he would never work with Kubrick again.
See the movie and see the documentary. It doesn't matter in which order (although I recommend seeing the movie first).