Does it matter? It was probably obvious to the scientists working on the bomb that other countries would get it too sooner or later, including countries at odds with each other.

Japan was better off in the long run being occupied solely by the US instead of a split occupation with the Soviets like Germany. If we hadn’t dropped the two bombs, the Soviets were set to invade northern Japan.

They were allies by necessity, but I don't think there were a lot of illusions about where things age heading. After all, the official doctrine of the Communist Party has always been that every non-communist regime has to be violently overthrown and replaced by a communist one. USSR didn't have the bomb not because they didn't want one, but because they were incapable of building one by themselves, and stealing all the details by means of vast spy network they had in the US, and then recreating them on their side, took time. If they had the capacity, they'd do it as fast as possible.