Truman didn't even know about atomic bombs and that we had created them until a few weeks AFTER he was sworn in as president.
Stalin knew about the Manhattan Project a year or more before Truman did.
Truman pulled Stalin aside at Potsdam, just the two of them and Stalin's translator. That's when Truman first "told" Stalin about the weapons. Of course, Stalin knew all about the project and that Russia had successfully infiltrated it. He probably knew more about the U.S. effort than Truman did.
“We dropped the bomb not to get Japan to surrender, but as a warning to the Soviets. Of course, we didn’t realize that by then the Russians had already stolen all the information they needed to make their own bomb.”
Nope, FDR gave him that data and the yellowcake needed to produce same during WWII.
Read “American Betrayal” by D. West for the details.