Hi there -- Truman did know about the Manhattan Project because he (among other congresspeople) had been investigating military waste and asking questions about spending, and came close to the project itself. This thread from an AMA with our resident nuclear expert, u/restricteddata, explains it better than I could, but essentially:

• Truman knew there was a big project for some sort of superweapon;

• Truman did not know/understand it involved fission, or the nature (size) of the weapon.