But if you're just basing that assumption on the visuals alone, then that would mean that the Enterprise looked like it did in "The Cage/The Menagerie,' then was refit into what we see in DSC/SNW, then would be refit again back to roughly how it looked in TOS. That doesn't make any sense.
The bottom line is that it was a creative choice to make the SNW Enterprise look the way it does, rather than making a 1:1 copy of the TOS version. This choice was based on the aesthetic of the previous show DSC, which went out of its way to look absolutely nothing like TOS. Just like it was a creative choice to make the Klingons in DSC look like Middle Earth orcs rather than how we've seen them since TMP (and ENT before that, chronologically speaking.) The thing is, in SNW they decided to go right back to the TMP/TNG/ENT Klingons and completely ignore the visual aesthetic created for DSC, just like they went back to showing a TOS Connie in PIC at the Starfleet Museum instead of using the SNW version.
To most fans, visuals don't matter. Only the story does. And that's fine. CBS certainly doesn't worry about the visuals. However, I personally care enough about the visuals to where I interpret shows like DSC and SNW to be part of a multiverse (which LDS showed was actually a thing), and that there's more than one 'prime' timeline (as also shown in LDS), and that terms like 'prime' are really just buzzwords at this point. (There are also more fundamental reasons why I consider DCS/SNW to be a different universe which does not seamlessly lead into TOS, but that's another story.)