Truman had no knowledge of the Manhattan project, he had to be read in after FDR died.
Truman had knowledge of it, but he had no information on exactly what they were doing. When he was a Senator he was in charge of a program targeting waste & fraud in defense spending. The program had the highest priority and was gobbling up billions of dollars. People started to notice. But when he started sniffing around, the best they could tell him was that it was the the highest secrecy and “trust us”. He wasn’t the only one, the consensus was sort of along the lines of “well, after the war you’re gonna have to have some answers and they better be good, or you’re going to jail”. In those days there was careful public accounting and politically speaking lawmakers faced consequences for misfeasance or malfeasance.
For all that, Truman wrote some things in his autobiography that tends to point to the fact he had a fairly good idea what they were up to.
The US government thought Germany was working on atomic weapons, though they were not, the Germans thought the US was working on rockets, which they were not.