Potsdam required the Soviets to aid in the defeat of Japan after Germany’s fall. It was getting clearer and clearer that had a longer war permitted Stalin to really, really contribute that a very stark division of Japan would be required, much as we saw Europe and Korea carved up.
Dropping the bomb would provide a quick way to keep Uncle Joe’s greedy mitts off of Japan.
The only really “Japanese” land Japan lost was not lost to America, nor to Britain, nor to Holland —they were AND ARE NOW lost to the Soviets, now Russia.
Japan wanted to keep it’s bureaucracy intact, and she knew if the Emperor system were preserved then she’d have that.
The American side knew if they dropped the bomb not only would countless American and Japanese lives be saved but the Soviets could also be cut out of the deal.
Japan’s overtures to Russia as a peace-deal broker fell on Stalin’s ears because Stalin DID want the type of longer war that would give a big part of Japan, or at least bigger than what he got (two small islands north of Hokkaido).
The Soviets pretended to be seriously considering this measured role of mediation but actually did nothing of the sort.
The only problem we have is that we haven’t used it since.
That may have to change in our war with Islam.
The Japanese also knew the Soviet army in East Asia was at the far end of the longest logistic train in all history, and believed the Americans had all they could do to supply their own forces.
However I am with you in believing the Russians would have played a significant roll in main island battles. As the battles became ever more brutal surely Stalin's legions would have been invited to be ground up in battle.