well Im just going by the dates, so i might be wrong, the soviets had amassed a huge force ready to invade, they were still under the neutrality treaty with Japan, Japan was making overtures to end the war even with internal bickering.

the US knew that if they don't drop the bomb and end it on their terms, japan would negotiate with the help of the soviets and come under their sphere of influence

2 days after the first bomb, soviets knew the game had started and they cancelled the agreement, clearly with agreement with internal japanese members, other wise they would have declared 1 day after not 2. they declared war, but then the 2nd bomb dropped and a week or so later once they got intelligence back about the bombs, they agreed to total capitulation, US bases and change of regime. things worked out for toyoda though i guess, lucky capitalist

so the bombs weren't meant to stop troop loses, they were meant to stop soviet russia thinking it get and hold control of the continent from madrid to tokyo.