Japan surrendered not because of the bombs, but because the US and the Soviets were on their doorstep. It’s like when the SWAT team is outside your house and puts tear gas through the window.

From my understanding, it was primarily the loss of all their forces and the widespread firebombing, with the increasing threat of Soviet invasion, and the nuclear bombs (to a lesser degree) just being the final nails in the coffin. That said, again, they had lost all their forces in battle already, so saying the war was won by bombing is also a stretch - its just that between the firebombing and the nukes, it was the closest to an example I could think of.