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.
I absolutely am fine with this take now, especially. Ultimately, what we are talking about is the narrative importance of the events. If we want to have episodes where the characters go to “today” today must continue to exist within the narrative. If the narrative says that the world was noticeably different in 1996 - move it to 2036. If we’re still going strong move it to 2056.
These changes don’t make as much difference in the narrative that was being told to begin with.