Up until the "modern era" of Trek, my understanding of canon is that the Eugenics War happened in the 1990s and was immediately followed by WW3. It seems like that has changed.
Picard season 2 took place in the 2020s, and there was no evidence of widespread devastation that would have taken place in a major war, although it could be argued that it wasn't shown to us on-screen. At the end of the series, we see a folder labeled "Project Kahn," hinting that either Kahn has yet to be born or that the season's "bad guy" is planning to continue Kahn's legacy.
In Strange New Worlds Season 2, Episode 3, the focus is on Kahn and how he affects the timeline. We see Kahn as a child, meaning the Eugenics War has yet to take place, even though the episode takes place in what is obviously 2020s or 2030s Toronto. Even more telling is that the Romulan spy says "This should have happened in 1993." Might have been 1992; still, early 1990s.
This leaves me with a few questions. If the Federation time-cops are so set on preserving the timeline, why did they allow the timeline to be altered to such a degree that the Eugenics War, a major event in Humanity's history, happened at least 30 years after it was supposed to. In addition, what event actually altered the timeline so that Kahn was born/created decades later than he should have been? As far as I remember, we haven't seen anything to show why this happened.
Since we now know from SNW that the Eugenics War happened some time after the 2020s, how does that fit into the timeline for Zefram Cochrane's first warp flight? Assuming the Eugenics War is still followed by WW3, that only leaves a max of 49 years between the start of 2 major conflicts and first contact with the Vulcans. In "First Contact," Cochrane and company assumed the Borg attack was from a hostile force on Earth. Perhaps WW3 was still in progress, and the events of 2069 were what ended the war?
On a side note, the destruction of a single ship spawned the Kelvin timeline. Since SNW shows us that events in Earth's history no longer match up with the timeline established in TOS, TNG, VOY, and DS9, does this mean that SNW (and possibly PIC) are also in a non-prime timeline?
Maybe they were unable or unwilling to stop it? Either it was from a time-incursion that they're not sure that they could interfere with, or it was something that, from their viewpoint, didn't actually cause any major issues, similar to Voyager arriving home several decades earlier thanks to Admiral Janeway's intervention, or Professor Rasmussen having his timeship stolen, and the thief going to the 24th century to steal technology and "invent" it in the 22nd.
I don't think that that would change much. All that really needs to happen for the same events to take place is some devastating conflict around the mid-21st century, and that's still plenty of time for Sloane and Cochrane to invent warp drive, and test it out thanks to some help from the future.
That's still plenty of time, especially if one thing lead to another. It's not implausible that the Eugenics War was a precursor conflict that went global. The gap between the Korean and Vietnam wars was only a single year. We know that at the very least, WW3 was a nuclear exchange, leading into the Atomic Horror, so it's not implausible that the actual WW3 conflict was extremely short.
I doubt it, but it's not implausible that that would be the conclusion that Cochrane and Company would leap to. They were used to WW3, and up to that point in time, aliens were not confirmed to exist. The most logical assumption would be that it was a hostile attack from another Earth force, rather than cybernetic grey men.
Cochrane and Co weren't military or government forces, either. They were civilians, which means that they would not be privy to any intelligence or evidence that might indicate the presence of aliens and inhabited life. Aliens would have no reason to start blowing up civilian infrastructure.
Personally, I think that the war continued for some time, and the Vulcan presence announcing themselves to various governments either put a stop to it as everyone scrambled to realise that aliens with superior firepower existed, or the Vulcans inserted themselves into Earth's leadership and ended the wars that way. Dangling the stick of comparatively advanced alien space-weapons would be a tempting prospect.
Alternatively, the war had already ended before 2069, and Cochrane was one of the survivors of the atomic horror.
No, time travel is strange and flexible. Sometimes the destruction, or non-destruction of a single ship, like the Enterprise-C alters the main timeline, sometimes it branches the timeline instead.
We know that from a production standpoint, at least, the Narada incursion was stated to have bidirectional effects on the timeline, so it is possible that the alternative timeline was created when the cumulative changes were too great to reconcile with it. At the very least, it is one of the few time-travel incidents, involving the future ending up in the past, that is not a closed loop.
Discovery S3 also suggests that the Kelvin timeline was also involved in the time war to some degree, which might have further complicated matters. If they also had their own time agents that were trying to maintain the Kelvin timeline's events (not unlikely), that might have also helped cement it off-screen, since it would no longer converge with the prime timeline.