I've had a head canon that SNW (and DSC) are a separate timeline from Prime Trek/LD/PIC for awhile, and honestly at this point its the only way to justify a bunch of the show, especially "Spock" and his relationship with T'Pring, which 100% goes against the spirit, if not the actual text, of what Amok Time seemed to say about their lack of relationship. The Gorn are also very obviously not the Gorn of Prime Trek (or the Mirrorverse or Kelvinverse).
Since Trek has a history of universe jumping, with both the Mirror Universe stuff and Prime Spock traveling to/creating the Kelvinverse, the Lower decks crossover can even easily be canon to both (Lower Decks, like Picard, being obviously still in the Prime timeline because of how specific, and how much, they connect to it).
I mean in the end its all going to be head canon. The people writing/producing SNW don't give a shit about continuity or the franchise in general, but if its even a little to their advantage to say SNW is canon with TOS/etc then they're going to keep saying it no matter how much they contradict everything that comes after them in the timeline.