Interesting article arguing the various viewpoints around this.

I do think the idea of using the bomb to deter the soviets is important, regardless of veracity, I think it's plausible.

https://ahf.nuclearmuseum.org/ahf/history/debate-over-japanese-surrender/

Additionally, I don't agree that the land invasion would have been bloody. If the USA was smart they would have continued the carpet bombing into submission and close air support of troops during and ahead of invasion. Airpower if used effectively can reduce friendly casualties dramatically as seen in desert storm