For starters, the USSR was only as effective as it was in WWII was Lend-Lease from the other Allied nations. They couldn't even have stopped the Nazis at Stalingrad without it. If the US and the UK stopped supplying them because they were engaging in an invasion of Japan, that invasion would have collapsed.
At war's end the Soviets Pacific fleet was a brown-water-only operation, ZERO blue water naval assets. And the Japanese already had handed their ass to them once in a naval battle earlier in the 20th Century.
So it's not as certain as all that that a Russian invasion even would have reached Japan.
Plus, the Japanese Army still was relatively intact because all the previous land battles had involved primarily naval infantry, not army. They were guarding the homeland and spoiling for a fight.
Plus, as the atomic bombings took place, the Japanese were training children as young as pre-schoolers to be ammunition bearers to help repulse the invasion.
The Japanese clearly were gearing up for a fight to the last man, and I don't think they would have cared whether the star on the invader's caps was silver or red.
The Japanese only stopped fighting because the Emperor took the extraordinary measure of telling them to in a radio address. Absent this, it's virtually certain the military commanders would have ordered their forces to keep fighting and tens of thousands of more Japanese would have died. Hirohito knew this and I think he ordered them to stop fighting out of compassion for his people, not out of fear of the Russians.
The only certainy is that we nuked them and they surrendered. Everything else is hindsight and speculation.
“So it’s not as certain as all that that a Russian invasion even would have reached Japan.”
Well that “brown water fleet” got them to South Sakhalin Island in mid August. Russia still holds that territory.
To the point of the original post for this thread: both bombs were needed, the Japanese understood the massive effort to produce just one bomb and were not convinced we had more than one until the second one was used, then they were unsure how many more we might have.
The Soviet invasion was also crucial, Japan had thought it would take Stalin much longer to amass forces in the Far East and were shocked when he started taking territory so soon.