It’s unreasonable to equate what happened in the south with what was done to Hiroshima and Nagasaki.
You are right. More people were killed in the South than Hiroshima or Nagasaki.
If you research the term “total war” it doesn't take long for the name of Sherman to pop up.
From Wikipedia: “One can trace back the phrase to the publication in 1935 of World War I memoir of German Genral Erich Ludendorff, Der Totale Krieg (”The Total War”). Some authors extend the concept back as far as classic work of Carl von Clausewitz, On War, as “absoluter Krieg”; however, different authors interpret the relevant passages in diverging ways.[3] Total war also describes the French “guerre à outrance” during the Franco-Prussian War.[4][5][6]
“During the American Civil War, Union General William Tecumseh Sherman stated that to win and end the war with fewest possible casualties, he must wage “hard war” (a synonym for total war) against not only enemy combatants but also enemy civilians on the home front who engaged in arms and food production for the war effort of the Confederacy. By destroying infrastructure vital to the Confederate war effort and striking a serious blow at civilian morale, he thought that it would seriously impair the ability of the Confederacy to continue resistance and thus would turn its populace against their leadership.[7] In his letter to his Chief of Staff, Union General Henry Halleck on 24 December 1864 described that the Union was “not only fighting hostile armies, but a hostile people, and must make old and young, rich and poor, feel the hard hand of war, as well as their organized armies,” defending Sherman's March to the Sea, the operation that inflicted widespread destruction of infrastructure in Georgia.[8]
The very next paragraph states: “United States Air Force General Curtis LeMay updated the concept for the nuclear age. In 1949, he first proposed that a total war in the nuclear age would consist of delivering the entire nuclear arsenal in a single overwhelming blow, going as far as “killing a nation”.[9]
Sherman never considered using nuclear weapons. He didn't have them. If you read Sherman's homicidal musings, however, it hard to image him being more restrained than President Truman - and Truman (by his own account) didn't hesitate to use nuclear weapons.
Dig hard and you will find some historian that will say Sherman's tactics “didn't quite reach” the technical definition of total war. I would hate to live on the difference.