The time-heals-itself concept is starting to grow on me
Sure, maybe Sera was an unreliable narrator, and it's just the USS Relativity working in the background to correct things (even if they end up happening a few years off from when they should).
But maybe in the time scale of millennia, it more or less evens out.
Khan comes to power later in the timeline, but DIS and SNW seem a little more modern than they should? Some things are slowed down, and others are sped up.
Why did they have to show Khan shifting into the future just one year after Picard and co. travelled back to the same time and we saw Soong on trial for the Khan project (a past event)? What benefit is there to jacking around with what they just established?
I don't think that changes anything that was previous established. Picard established that Soong did illegal genetic experiments, but it does not stipulate that his experiments were illegal because of a prior genetic research ban. Soong later recovers the 1996 Khan Project file.
My take is that Romulan time agents went back in time to hide the Khan file. They perhaps moved Soong away from that avenue of research not knowing how the Confederation would play into it. In any case it didn't work because Picard did his own time shenanigans pushing Soong to take more drastic measures.
In less than a year the Khan project has found a new home in Canada with new research partners. The Noonien-Singh Institute has Adam Soong's fingerprints on it somewhere, but it's unclear where. In any case whether there is a connection or not, Soong discovers the Khan project from 1996 in 2023. In SNW the Khan project has only just begun a year later and already has found its Khan.
It still seems like they could have coordinated the two plots in a more transparent way, given that the shows are running concurrently and have overlapping staff. Fans shouldn't have to do this much mental gymnastics to reconcile episodes that aired two years apart. The in-universe claim that the pre-history of our era is constantly shifting seems like a cop-out in those circumstances.