I mean, everyone who insists that the ship "always" looked like the SNW aesthetics is inadvertently admitting it's a "close enough" alternate timeline where somehow the aesthetics must have changed. I think it's all the same timeline and that's why I claim there's some offscreen refit between SNW and TOS.
As it is, there's now the major bit that the Eugenics Wars happened at least 40 years later than originally occurred, although this only affects the dialogue in Space Seed and WoK.
(As for Cage and Q&A and Menagerie, I'm kind of pretending that the holdover from the mind-affecting Rigel mission messed with the crew's perception of the ship and this carried over into the Talosians' illusion in Menagerie, but I admit this is a stretch).