The terms are irrelevant, because the US did not get an unconditional surrender in your all-embracing sense. It got a capitulation with the understanding that the Emperor was not threatened (which was indeed subsequently the case), which makes sense once you understand that the 'unconditional surrender' in the Potsdam Declaration was only about the military forces:

"We call upon the government of Japan to proclaim now the unconditional surrender of all Japanese armed forces, and to provide proper and adequate assurances of their good faith in such action. The alternative for Japan is prompt and utter destruction."

The question is why the Japanese government abandoned its previous insistence on a general admission of defeat with 4 conditions and settled for just 1 condition which was acceptable to the US since it was not a military condition. And the reason for the dropping seems to have in large part been the sudden shock of negotiations with Russia failing and it dropping neutrality and starting its invasion. Even despite its almost immediate surrender to the US, Japan still lost Sakhalin.

(I'd note that we might expect claims about the necessity of the bombings to be overblown for at least 2 reasons: first and most obviously, it is important so as to justify the murder of hundreds of thousands of civilians in those bombings and other ongoing campaigns despite US government awareness of Japan's ongoing surrender overtures and that Russia would switch its attention to the Japanese front soon with what were probably at the time predictable consequences, and secondly, it is a useful claim in minimizing credit for the Russian contribution to WWII, a phenomenon already acknowledged about most US treatments of the European theater's eastern front.)