The second bomb was unnecessary as surrender talks were already underway.
This statement contradicts everything I have ever read or watched about WWII. There is no support for this on Wikipedia (which clearly states that the emperor interceded after the second nuke), or anywhere else that I can find. Do you have a citation for this claim that "surrender talks were already underway"?
In July, the Japanese had tried to enlist the Soviets as an intermediary to negotiate an end to the war. But no talks were started because the Soviets were already making secret plans to abrogate the friendship pact and attack the Japanese in Manchuria and Sakhalin.
Even after the second nuke, a majority of the Japanese cabinet supported continuing the war. In his memoirs, Mitsumasa Yonai, the Japanese naval minister and close adviser to the emperor, described the bombings as a "divine gift" because they gave the emperor a face saving way to end the war. He felt that otherwise the war would have otherwise dragged on, with disastrous consequences for the Japanese people.