Two things:

1. In “A Quality of Mercy”, we know that Una loses her trial (in that episode’s timeline). In “Ad Astra Per Aspera” we see that Pike takes some unusual steps to secure the win. The only difference between the two trials is that in the second case, Pike has knowledge from the future which influences his actions in the present.
2. In “Tomorrow and Tomorrow and Tomorrow”, we see that Khan does not wage the Eugenics Wars in the 1990’s, but instead during the 21st century. It’s a minor detail, really, but at the same time it’s a clear and deliberate diversion from the original series (where Khan and the wars definitely did happen in the 1990’s).