They directly asked a pilot, under torture, how many nuclear weapons the US had at the time. They were early concerned on some level. The pilot even lied and said they had hundreds of bombs (torture works, clearly) and even then some of the council didn't want to surrender non-conditionally or at all.

And the Soviets invaded after Hiroshima had already happened so I'm not sure the timeline works there. Not say the invasion didn't also have an effect on the decision to surrender.

War Minister Anami even seemed to desire nuclear devastation when the alternative was surrender, saying "Would it not be wondrous for this whole nation to be destroyed like a beautiful flower?", and eventually committing seppukku after the surrender.

Eventually, after an attempted coup d'état, Japan surrendered unconditionally. The attempts to surrender before were an attempt to gain favourable conditions for their empire and they expected to get them from Moscow, which is why the invasion was so shocking to them as well.

The use of these weapons is horrific, doubly so against what truthfully was a civilian target, but I don't really buy the idea that the Japanese were just secretly willing to surrender but just couldn't for whatever reason.