Late to this but I'm guessing that Stamets and Culber on the memorial wall was from the cover story that Discovery was destroyed in the 23rd century and all hands lost, and when Discovery showed up alive in the 32nd century they just never bothered to change it? Which kind of goes against Vance's claim that he never heard of Discovery in Disco S3 if they still had records of 2 of their officers being killed with Discovery (or he didn't even bother to do a basic database search).
Not keen on Nog listed as lieutenant, at least let him get to captain like STO did. I'm guessing he might've been killed in Vau N'akat fleet massacre in Prodigy.
Erica Ortegas and La'an being listed as lieutenants doesn't look good for Strange New Worlds honestly. Also, if they do die at the end of SNW, considering that Pike saw them alive in the Quality of Mercy timeline, Pike will then have to live with the fact that his "sefless" act to go through with the delta radiation accident gets two of his friends killed early. Although La'an dying in Starfleet service might be what helps trigger Khan's rampage in Space Seed when he reads about it on the Enterprise computer. It might also revert Spock from the rather chipper emotional fellow in SNW to the withdrawn, very cold, non-emotional guy at the start of TOS, so at least that explanation will be provided.