IMO it comes down to Hirohito telling the military "OK, We're done - time to stop." The successive nuclear strikes had a bearing on his change of mind.

In turn, the Soviet army massing across the Sea of Japan had a bearing on Truman's decision to OK the bombing. It's unclear how well he understood what they were. The US was already doing to many Japanese cities what they'd done to Dresden - Truman might have thought of the one for Hiroshima as 'just a bigger bomb'. It's not clear he understood (and could have halted the bombing) before Nagasaki. there's no evidence he tried, but his focus was more on first avoiding a huge number of US casualties and second the expanding 'Iron Curtain'.

FWIW. yeah, I've read a lot of history, don't consider myself to be a 'military historian'. My focus had been more on Ancient/Classical (e.g. Herodotus, Thucydides, Xenophon, Livy, Suetonius, et al) but my next door neighbor's dad is a professor emeritus of history, specializing on the Cold War. Gotta admit that period's beyond interesting - so I've dug into WWII a bit as well...