The U.S.A. would have kept dropping atomic bombs on Japan until they surrendered or there was nothing left of Japan. Instantly, after the successful Trinity Test, one million American lives were no longer at stake.
The U.S.A. didn't stop with the plutonium bomb that destroyed Nagasaki. We built more than 100 "Fat Man" type bombs before 1950 and only quit building them because we had better bombs.
In too many disturbing ways the destruction of Nagasaki was an experiment. Some factions in the U.S.A. wanted to see what these plutonium bombs could do.
U-235 gun bombs, like the bomb that that destroyed Hiroshima, were too expensive, and just too damned scary as weapons. They could go off by accident. Oops. Mushroom cloud. One less military base.
But mostly it was the money.
Many people don't recognize the scale of the Manhattan Project. The goal shifted, from fighting an all-out nuclear war with Germany to world domination.
Thus the subsequent horror when other nations, starting with the Soviet Union, built their own bombs.
They would have done it anyways, even without espionage. That's the way science works.
You ask the right question, you do the right experiment, and you get your answer.