A youtuber I follow on stream today was talking about how there were early talks between the Soviets and the Germans for the Soviets to straight up join the Axis powers, and he was imagining how uncertain victory might have been in such conditions; one thing he settled on was the worry about the race for nuclear weapons in the European front. Now from what I recall the Germans had expelled most of their atomic scientists for being Jewish and I don't know how advanced a Russian nuclear program would have been if they were waging a purely offensive war, but assuming America did certainly get the atomic bomb first how far could we have leveraged that asset? If we imagine an alternate world where the Germans and Soviets were working together to hold the beaches of Normandy instead of Russians draining manpower from the Germans that a nuclear bombing campaign might have been utterly essential for the destruction of fascism, but would we have been able to do it? I thought I heard somewhere that after we dropped the second bomb on Japan we basically didn't have any more to follow up with.
Well I can't speculate on this particular scenario but I can tell you that a) the Germans had no nuclear weapons production program to speak of (they had a modest reactor pilot program), b) the Soviets were too ravaged by the war to do any real nuclear work until after it ended, and c) the US Manhattan Project production system was such that from late July 1945 onward they were capable of producing the fissile material (nuclear fuel) for about 3.5 bombs per month (of the sort that they used on Hiroshima and Nagasaki). There are changes they could have made to the bomb design that might have stretched that a bit (e.g. doubled it or so). But that is about the extent of their atomic bomb production capabilities during the war.
On the question of "did they have more bombs for Japan after Nagasaki?", see here.