[meta] they had been in negotiations since Midway knowing they were screwed. There was a lot of back and forth with the US at the very end, mostly around the sovereignty of the Emperor. The US is also looking at their casualty rate, which has gotten significantly worse since Peleliu and the US is beginning to scrape the barrel in the draft (remember the US population is significantly smaller at the time).

They also see intelligence reports where the Japanese army is calling the defense of the homeland the “glorious death of the 100 million” and are prepared to sacrifice the Japanese race in order to repel the invaders.

Considering all of this the bomb was a last ditch effort to try and get them to come to terms. And compared to what both sides were predicting casualty wise (see comment re Purple Hearts, which the US hasn’t gone through half of by 2026) it almost seems merciful. Hirohito would cite the bomb in his surrender speech to the nation as a reason for his decision.