It’s looking like the broad strokes of Trek canon (specifically with respect to “The Cage” and “The Menagerie”) will be respected in
SNW. Indeed, the basics were already established in season 2 of
DISCO: Pike is in command of Enterprise; Number One is his first officer; Spock is a junior officer; etc. And in terms of apparent deviations… well, there’s narrative wiggle room. E.g., though Uhura wasn’t seen in “The Cage,” she might have been elsewhere on Enterprise.

Or, at some point, she might have transferred off Enterprise and then transferred back on when Kirk took command. IOW, there are plausible scenarios that don’t explicitly contradict canon.
When
DISCO first launched, there were complaints about retconning Spock’s backstory to give him an adopted sister — a sister that Spock
never mentioned. (Of course, Spock never mentioned having a half-brother until one showed up in
Star Trek V.

) Eventually, however, we were provided an explanation as to why Burnham and Discovery were erased from official Star Fleet history.
Likewise, in
SNW, it’s possible that what
seems non-canonical will — eventually — be set straight.