I don’t want to get too sidetracked here, but in short: No. Producers and writers have strongly emphasized that this is the original timeline/reality, but with different production design. It’s the same universe, seen through a different lens, much like how production design for TMP looked very different from TOS, and First Contact very different from “Encounter at Farpoint” (more different than would be explained by 10 years).
The philosophy seems to be analogous to that of Enterprise in many ways, which took technology of 2000 and moved it forward 150 years. I remember that being very upsetting to some of the audience. To me it feels like Discovery’s production design took the tech and designs of Enterprise (itself informed by the real-world advances since the 1960s), and moved them forward 100 years, while taking certain influence from TOS and TMP-era work. Whether people agree with this approach or not, that is just how it is.
In addition, something that is a key driving force of the plot for this arc confirms this mirror universe must be the same as that seen in TOS and Enterprise. And that “something” (not saying specifically for spoilers) was shown briefly, with design tweaks from what was seen in the other shows, though the changes seem less drastic than other production design changes.