World War III is the establishing event in the Killzone timeline. The war was waged over diminishing fossil fuels in 2055, and saw widespread use of nuclear weaponry. At first, exchanges were limited to tactical-scale nuclear weapons used on the battlefield, but as the war progressed, it soon escalated to the largest and most devastating of nukes being launched en-masse at major population centers.
Seeing the sheer scale of destruction being wrought before them, the remaining world powers began peace negotiations in a successful effort to prevent further damage. This peaceful period marked the development of advanced space-faring and habitation technologies that would enable humanity to quickly traverse other star systems and colonize distant worlds, eventually forming the current setting of the Killzone universe. It also saw the formation of an interstellar government, the UCN.
While it is not mentioned how severe the exchange of nuclear warheads was, it was likely within the confines of 100 - 500 nuclear warheads being fired at civilian population centers, which would cause a "mini" nuclear winter, lasting around a decade. This would block roughly 40% to 70% of the sunlight from reaching Earth, causing severe reduction, but not complete elimination, of food and clean water. Any number of warheads less than this would not have diminished Earths resources to the point of requiring the colonization of other planets, and any more than that would have exterminated humanity entirely through a long, total nuclear winter, followed by the even deadlier nuclear summer, which would completely eradicate all life on Earth. This is the exterme while it is mentioned that all resources were devoted to space colonization its unknown if the damage was limited to a few major cities, and many capital cities of Earth were targeted by Stahl. If these cities survived or were rebuilt is unknown. It is safe to assume any damage done by the war has since been repaired as of the events of Killzone 1.