The history of Earth's world wars in Star Trek is very confused. Since Spock said that thirty seven million were killed the Third World War and Star Trek: First Contact says that six hundred million were killed in the Third World War - about 16.2 times as many - it seems obvious to me that there are two different numbering systems for world wars and that the system in First Contact has at least one fewer world war than the list Spock used.
"Space Seed" shows that the Eugenics Wars happened in in the mid 1990s in the "Space Seed" calendar and that interplanetary travel was very slow until about the year 2018 SS when space flight became much faster. Spock says that whole populations were bombed out of existence in the Eugenics wars - which implies that a lot more people were killed in them than in Spock's third world war - and that the Eugenics Wars were Earth's last world War, and thus World War IV or higher in his list.
Star Trek: First Contact shows Cochrane's first warp test flight in 2063 First Contact calendar, followed by first contact with the Vulcans, which leads to Earth rebuilding itself after the Third World War and eventually building warp drive starships. Since this is about a decade after the Third World War, that should have happened about 2053 FC. Since first contact lead to a glorious new future without any later world wars, and since Earth started building war drive ships soon after first contact, The Third World War in Star Trek: First Contact must be the same as the Eugenics Wars.
If you put the Eugenics Wars in 1995 SS and The Third World War in 2053 FC, the year one SS must be in the year 58 FC, and year 2018 SS, when space travel became much faster, must be the year 2076 FC, which is 13 years after first contact, surprisingly long.
But I don't write Star Trek, I only analyze the chronological data.
So in Picard's era Khan would be remembered as one of the main leaders in the terribly devastating world war which killed 600,000,000 people. It is true that Khan was not the aggressor but was attacked by other powers. But do you think that in Picard's era the fact that Roosevelt and Churchill were not the aggressors makes them seem like good guys, or do you think that TNG era historians say that Roosevelt and Churchill's war crimes with mass bombings of civilians set an example for the bombings of entire populations out of existence by Khan and/or his enemies during the Eugenics Wars?
I can easily believe that in Picard's era historians might may say that however good Roosevelt, Churchill, and Khan Singh were otherwise, in war they were war criminals and mass murderers.