I just can't think of them being in the same universe because the tech in this is so much beyond anything they had in TOS.
My issue with this (common) criticism, is that warp drive and transporters aside, the tech we have NOW is beyond TOS! Discovery is "the future imagined from a 2018 perspective" whilst TOS was "the future imagined from a 1960s perspective".
I've recently been watching a lot of TNG, and there's an episode where the big reveal is that the computer has been infected with a program that is spreading from system to system .. almost like ... a virus - cutting edge in the 80s, but now you just wonder why they don't have any anti-malware running.
While I largely agree with that, I found myself puzzled by the prevalence of holographic communications technology in Discovery. I don’t really have an issue with holographic tech existing in this time period, but it does seem to be used too much here. In the recent episode, a bloke accuses Captain Pike of being like his grandmother by ‘communicating by screen’. They ALWAYS communicated via screen, even in the spin-off shows! Holographic communication became a larger thing in the later series of DS9 and that seemed to be only for specific situations.
I’d just about buy the idea that they used holographic communication on Discovery due to it being a cutting edge science vessel* but that reference from the prison bloke in episode 3 suggested all the hip kids were using it.
*not too much of a stretch. One of the lecturers at my university mentioned ‘blue ray technology’ and even gave me a good layman’s understanding of it. This was just before ordinary DVDs came out (or maybe they’d just come out? I don’t think so, though) and a good few years (maybe even a decade) before blu-Ray actually appeared.