So there are a few aspects to this that are worth breaking down.

First, did several high-ranking military commanders after the fact argue that the atomic bombings were unnecessary? Yes! But it's not as simple as saying, "and thus they were unnecessary." The military commanders in question voiced such misgivings only well after the fact (the initial Eisenhower anecdote quoted from his memoir cannot be substantiated and probably never occurred), and in all cases the undertone is, "the atomic bombs weren't necessary because our conventional forces had already beaten Japan" — it is about credit for the military generals in question, who were not involved in the making of the atomic bomb, and their resentment of the bomb getting so much attention. These comments came as Truman was attempting to use atomic weapons as an excuse to cut back the conventional forces. So one needs to contextualize them and take them with a grain of salt. It does not mean that they didn't believe these things (they had good, self-serving reasons to), but there is a difference between concluding that they were correct. The fact that these same people very much made their peace with the use of atomic bombs later is a further indication of the complicated politics of the bomb and the military from the 1940s-1950s (once it became clear that the US was not going to cut conventional forces, suddenly the military brass became very amenable to nuclear weapons).

Second, were there Japanese peace feelers at various points in the war? Yes! But these are not the same things as actionable offers to surrender, and when you look at these "feelers" it is important to recognize that they were being offered by a minority faction within the Japanese high command. The Japanese Supreme War Council was dominated by militarists who were absolutely opposed to any surrender, even a "conditional" surrender. Their reasoning varied on this from the coldly-calculating to the absolutely-delusional, but either way, they were not interested in it. There was a minority faction, whom the Emperor had a lot of sympathy for and gave some tacit support, who were interested in a negotiated, "conditional" surrender. These are the people sending out peace feelers, looking into the possibility of some way to end the war that would be acceptable to them, if not the militarists. The US rebuffed these feelers; they did not think that the people offering them had the power to follow-up on them if they were pursued (again, they were a minority group), and, for various reasons, both Roosevelt and Truman insisted on unconditional surrender anyway. So, to summarize, the peace feelers were not sanctioned offers by the Japanese Supreme War Council, and so were not likely representative of what the Japanese would be willing to do anyway, and they were also conditional surrender offers, which the US was inclined to reject anyway.

Even in July 1945, the "peace" party Japanese were trying to convince the USSR to broker negotiations for a conditional surrender with the US — the US knew of this through decryptions, and interpreted it, not entirely wrongly, as indicating that the Japanese were still not ready to accept unconditional surrender. Even after the atomic bombings and Soviet invasion, the Japanese still first offered a conditional surrender — it was only the refusal, then, and an attempted coup, that led to their final surrender agreement. Which is to say, the Japanese found it very hard to end the war internally, though there were some (including the Emperor) who realized this was necessary. It was not as simple as the "they offered peace, thus the war was prolonged for no reason" advocates tend to make it out to be.

Was the US insistent on unconditional surrender a factor on prolonging the war? Potentially so, and people have argued that since the 1940s, anyway. There were various arguments made in favor of the unconditional surrender requirements, including "this is payback for Pearl Harbor," as well as "if you give them an inch, they'll ask for a mile" (a more strategic approach). I think it is again worth noting that only a minority faction within the Japanese Supreme War Council was willing to contemplate a very minimum condition (protect the Emperor and the Imperial House) before August 1945. As it was, the US did preserve the Japanese Emperor/Imperial House (with some big modifications, like requiring the Emperor to renounce his divinity), but that was a decision they made much later under the conditions of turning Japan into a reliable ally, not forcing them to surrender; it does not really follow that they could have necessarily achieved surrender by adopting the leniency that they did later, after surrender (I'm not saying it is impossible, just that it does not follow logically that these should be necessarily equivalent).

Now, none of the above should be read as me advocating that the US needed to use the atomic bombs to end the war, or that it needed to drop two bombs on two cities in three days to achieve the result it got. There were other alternatives on the table at the time and it's possible that the same results could have been achieved through these approaches as well. It is incredibly hard to say one way or another in retrospect, because history is not a simulation you can just re-run with different variables, and because the end of the war was in fact extremely complicated. The role of the atomic bombings in the end of the war is something that has been long-debated by historians and is likely to be unanswerable.

That is a different set of assertions and questions than whether or not US military leaders thought the bombs were unnecessary, or whether there were Japanese peace feelers on offer. These things are true — but more qualified in their meaning than many articles about them make them out to be. The unfortunate truth is that most of the scholarship on the atomic bombings is pre-committed to one conclusion or another (they weren't necessary, they were necessary) and you can see that when you look through their arguments and sources and the way they omit certain things to fit their narrative better. The reality as I see it is that these things are pretty complicated and there are a lot of things that are, I suspect, fundamentally unknowable, but that is a conclusion that is not very satisfying, and does not fit into a pre-determined political conclusion, and so is a lot less represented.

Does the article present some true statements? It does! Does it present all of the context around them (much less reflect the fact that historians have been arguing about this, inconclusively, for decades)? Not entirely.