Were US decision makers aware of the destructiveness of the Bomb of Nagasaki?

Were US decision makers aware of the destructiveness of the Bomb of Nagasaki?

Must I assume that US leaders were well aware of the destruction they ordered?

Absolutely.

There might have been uncertainty about the effectiveness of the Little Boy (uranium, gun) design. It was untested, after all, and the effects of a nuclear airburst over a city were not yet well understood.

But Little Boy produced a yield of ~16kt, comparable to the ~20kt yield of the Trinity test, and there could have been little doubt that the effects of Fat Man dropped on another city would be comparable to the effects of Little Boy on Hiroshima.

(Which, given that there was a B-29 accompaning the Enola Gay for the expressed purpose of photographing the effects, and assuming there were recon flights in subsequent days as well, would be documented well enough.)

So, yes, the decision makers would have been well aware of the scale of destruction that would result from that second drop.

The unfortunate addition of the word "perfectly" before aware means no, and it really depends on who you define as "decision makers" and what you mean by "aware".

First off, here is a great academic (but highly readable) blog run by a guy named Alex Wellerstein with lots of discussion about nuclear weapons in general, but with lots of emphasis on the decision to use the weapons in World War 2 in particular (obviously). It's especially great because he's got lots of contemporary documents that reflected how the participants thought at the time, as opposed to later when they are trying to smooth out their thoughts for historical purposes. I'll reference the titles of specific posts as I go for footnoting.

To answer the second question about awareness, many of the senior scientists and military officers involved in the Manhattan project certainly understood the damage of heat and blast (overpressure) could cause, because they used this when designing the bombs and setting the altimeters such that they could inflict the most possible damage from those effects, specifically on Japanese cities, which featured many buildings of light construction. See the post "The Trouble With Airbursts" and "The Height of the Bomb" for more info. As far as radiation sickness goes, certainly some of the scientists were aware, but Oppenheimer didn't seem to care about it, which meant General Groves knew nothing about it, and you can cut the farther chain above (Secretary of War Stimson and President Truman) from any knowledge whatsoever. See the post "Who Knew About Radiation Sickness, and When." As the post "To Demonstrate or Not to Demonstrate" discusses, people in Los Alamos themselves hadn't entirely come to appreciate that these would mean a truly new era of warfare until after the war. Especially for Truman, he understood he had a very powerful and destructive weapon he could use, but his understanding doesn't go much further than that. The post "The Kyoto Misconception" discusses how Truman seems to have been confused about how much damage the bomb would cause and what kind of targets it would be used on (Truman thought they would be used on purely military targets, not appreciating that Hiroshima and Nagasaki both were certainly not pure targets-they would have been firebombed long before if they had). The overall view could be summarized as they largely (if not entirely) thought of the A-Bomb as a weapon that combined the best of massive conventional payloads with incredible incendiary effects in one very efficient package that would be impossible to stop without massive effort from the defenders. They didn't fully realize how different it was until after the bombs. As "Hiroshima at 67: The Line We Crossed" notes, the line crossed wasn't one of using nuclear weaponry or not, it was one of non-precision targeting of cities-and that line had already been crossed with regards to Japan.

Finally, we can come back to the question of decision making, and in this case, who were the important decision makers, and the answer is mostly Groves and President Roosevelt (though how much he knew is an unknowable question since he died before the project yielded real results. It's noteworthy he inquired about using the bombs against Germany during the Battle of the Bulge, only to be told that they weren't ready and wouldn't be for some time). While the traditional view is that Truman was also important in the decision-making process, one fair thing that modern history has done a good job of noticing Truman didn't make a decision in the sense of either "Use the Bomb or Do [Insert Alternative Here]", it was more of a "Didn't Stop a Decision that had already been made before he came into office". As Wellerstein notes in a couple of places, Truman would probably never have thought of NOT using the bomb. His most important decision, as noted in both "The Kyoto Misconception" and "Why Nagasaki", was to stop the bombing after Nagasaki (although it didn't matter, since they wouldn't have had a 3rd shot available until much later anyway). Stimson's role is to screen out targets (as noted by removing Kyoto).