Seldom do such "history" look at for the bomb take into account the Soviet declaration of war against Japan - a deal struck between FDR and Stalin long before. Yes, two bombs were dropped and a third was being readied - some historical accounts give Truman credit for stopping that one; it's possible. And then the Soviets declared war and Japan turned to the US to surrender on whatever terms the US set.
There were multiple things occurring at the time- like the Emperor wanting to surrender and being basically locked in his castle by military leaders who did want to fight to the last person. The Emperor recorded his surrender on vinyl- 3 records which were smuggled out.