« A cover story for what ? » — To cover up dozens of heinous mass-murdering crimes with veneration of “the Bomb” ?
« We have eyewitnesses of Hiroshima. » — Yes, we do. You'll find some in the Palmer book (link in the dead comments). You'll also find some in chapter 19 of the Rhodes book (The Making of the Atomic Bomb), where they're more numerous but less interesting, as the book serves a different purpose: it's not an investigation, but a narrative. About 60 % of the eyewitnesses Rhodes quotes were children, and what we have is their recollection decades later. Let me quote this:
A five-year-old girl: The whole city … was
burning. Black smoke was billowing up and we
could hear the sound of big things exploding.
« We have videos of atomic bomb tests. » — Those are separate incidents.
« Multiple countries … Why ? » — You're rushing to ulterior questions, if not to conclusions. Palmer focuses on the Hiroshima and Nagasaki evidence. And there is more than enough in there already that is “puzzling”, to reuse your expression. So I'd prefer to stay focused.