Discovery has itself provided proof it is not from the Prime universe.
I bring your attention to DS9, “The Changing Face of Evil” (season 7 episode 20).
Time index (DVD) 4:06
General Martok states to Captain Sisko after seeing the Breen attacked Earth, “even my people never attempted that” yet in the final episode of Discovery, there is a Klingon armada within striking distance of Earth.
This isn’t a discrepancy that can be reconciled any other way.
I haven’t seen it yet, just a few minutes of it.
I rather like the Mirror version of Captain Georgiou, she’s direct and doesn’t take $&!#, Sisko and Janeway amped up with a twinge of cruelty mixed in. Might just get the job done.