The first things to remember about the Oppenheimer movie is that the parts of the movie in colours represents Oppenheimer subjective point of view, and the parts in black and white are meant to be objective.
So for the “why did they bombed Japan?”
The movie presents/tells explicitly that it’s because the number of casualties were going to be less than the alternatives. The bombs were made not to bomb cities, but to end the war. Which they did.
(historically, you need to remember that in addition WWII was a total war, and that nothing but an unconditional surrender of the Empire of Japan would have been accepted)
Now for the “why is it Oppenheimer’s fault?”
This is the entire message of the movie.
The movie seems to show Oppenheimer as embodying nuclear anxiety/guilt.
There is moment during the second half of the movie, during the hearings, where Oppenheimer is showed in conversation by a lake with Einstein. A fact observed from a distance by Strauss. This is showed in black and white.
Ambiguously it is left open if the conversation was about the hearings, Strauss, the personal, and the political. As Strauss thinks, and express. Or something else.
The last scene of the movie is a return to this conversation. In colours. And the conversation is showed to be about the bombs, what will follow it, and what it means for humanity.
I think that’s the message of the movie. The subject is Oppenheimer, the message is that guilt and anxiety ended up defining him.
Oppenheimer blames himself, it’s not objectively his fault. But it is for him. Again the black and white and colours.
In the movie, after the trinity test he keeps having hallucination (or least thoughts represented by hallucinations) of the results/casualties of a bomb. And he his haunted by them.
It showed to be, at first, a really primal reaction.
In the end he tries to bring more, and rationalise it. Which does not help him, and just makes his regrets more educated. He basically foresee the cold war, and fear of nuclear annihilation.
I also think it will be interesting to see the parallel made by the movie between the creation of the bomb, and the romance/affair he had with Jean Tatlock.
The famous quote from the Bhagavad Vita is introduced by her after they sleep together,
It’s ending with a suicide, due to clinical depression.
And when he is plagued by guilt over it, he is told by his wife that it wasn’t his fault, and should move on.
Which in a way, the movie presents as true.
She is instigator, the movie puts attention that she calls him, he just can’t help answering. He was a participant of her life, and was a bit reckless, but he is not presented as the cause of the suicide, it’s a tragic spiral of its own.
Also saw Barbie, I recommand.