> it was believed at the time that German scientists were also very close to producing a nuclear weapon.

Yes this was the prime motivator, at least on paper. One can suspect Vannevar Bush or Leslie Groves of ulterior motives (Vannevar: fomenting a defense-fueled ‘Big Science’ infrastructure which he certainly achieved going into the postwar, Groves: creating a weapon to fend off the Soviets for the postwar).

> As was later discovered after the war, there were not.

Man this is a dicy one. There has been some scholarship in recent decades that the Germans may have got a lot farther than history has hitherto accepted to date, all the way up to minor (semi-fizzled?) detonations. Rainer Karlsch has been the main accumulator of relevant archives especially from the Soviet side. Todd Rider formerly of MIT’s Lincoln Lab has done yeoman’s work in piecing together the logic of Karlsch’a work and archive digging of his own & volunteers’. In short, we are not sitting on a consensus reality of just how far the Germans got in developing an atomic bomb, and we aren’t 100% certain on how little we relied on recuped German know-how in developing our own atomic bomb between May-August 1945, not how much we (ahem, Teller) may have relied in part on German know-how in developing the H-bomb. As I mentioned in another comment, the reference for this is

https://riderinstitute.org/revolutionary-innovation/#chapter...

Appendix D is the main one for this topic, and Chapter 8 for context.