To answer your question about how widely known it was: it was not widely known. But by the early summer of 1945 the very top level commanders (e.g. Marshall, Leahy, Arnold, etc.) knew about it. Prior to the Trinity test it was not at all incorporated strategically into plans because it was still unclear whether it would work or not. Even after Trinity, it was not incorporated in any really concrete way — there was no relationship between it and the invasion planning, for example, which was considered entirely independent. (The only coordination attempts came after Hiroshima and Nagasaki, where there was some thought as to whether to use atomic bombs to aid in the invasion.)

After the Trinity test, it was assumed the bomb was going to be dropped in early August. But if the question is, did they assume they did not need to invade because of the bomb? The answer is no: the plan was to bomb and invade, if need be. The bomb did not put any hiccup into the invasion plans (in fact, the only thing that did put a hiccup in them was Japan surrendering, which caught a lot of people off-guard with its rapidity).

For the Soviet invasion question, see the other comment about Hasegawa and his thesis.

Hi there -- while there's a lot to be said on this subject, you may be interested in this section of our FAQ, particularly the AMA at the top by u/restricteddata and his discussion of Hasegawa's "Racing the Enemy" at the bottom (also contributed to by u/ParkSungJun).