That would make sense, either having Eugenics Wars be another name for World War III, or maybe even a single theater within the larger war, much like how many sources refer to the Japanese front of WWII as the Pacific War.
They could also be the flashpoint that starts it, or combine with Optimum at the end of it, or we could be seeing the provoking incident of both Optimum,
and the Eugenics war with what's going on with the Borg Queen and Soong's ancestor.
There's also elements of "No Fate but what you make" going on. In TOS, the third world war happened in the 1990s, in TNG, it was the mid-21st century. There's temporal shenanigans that altered that timeline from Gary Seven to Kirk kidnapping a couple whales, to Picard's FIRST trip to the distant past (meeting Cochrane) not to mention Janeway's temporal interactions, Sisko replacing Gabriel Bell, and the Temporal Cold War's multiple visits by both sides in the Enterprise run, and now we've got Picard BACK in the past.
What if the reason Q is an antagonist this time, is because all of those have had a cumulative impact of both delaying the Eugenics wars,
and altering the logical outcomes (and delaying humanity's warp drive)?
Drop a rock in a river, the river diverts around the rock. Drop enough rocks in a river, and you've got a dam and the river changes course. There's been a LOT of rocks dropped in the river.
