Why do I bother. But here I go again.
Visuals are not narrative continuity unless that visual is intrinsically important to the story in that specific format. Hamlet is hamlet no matter if he wears a red shirt or a green shirt or body paint and a rocking codpiece. Hamlet does need to pick up Yorik's skull and not an empty water bottle, however. But the skull prop can be any old skull you happen to have backstage. If Trek fans were Shakespeare fans they'd be measuring the jaw line and checking teeth count to make sure it was a canon skull.
Enterprise did indeed show a 60's era set. I happen to like TOS and I like those sets, more for nostalgia. But Season 4 of enterprise was about throwing extremely well made cupcakes to an audience that had been handed a lot of plain toast for too long and probably wasn't going to get any more trek for a long while. It was awesome. But you can move on with out accepting some of the things that occurred in it as a roadblock to accepting anything else later. just a show.
By your logic, Where No Man Has Gone Before takes place in a different reality from the Cage or later episodes because the uniforms are out of place. I can't convince you of this. If you want it to be an alternate reality, fine.
Um... no. In 2254 during The Cage you have a uniform design, a ship design, etc. In WNMHGB you have a very similar uniform, ship, etc. It's been over 10 years so things have changed. Then between WNMHGB and The Corbomite Maneuver, the ship gets a refit and the uniforms are completely changed, as well as the phasers. It all fits nicely together. Then you have Enterprise revisit that and show us basically the same thing. Visually identical to what we'd seen before. As we also saw in TNG Relics and DS9 Trials and Tribbleations.
Skip to today. We have a big network now owning the property and no one seems to care about continuity and a show set between The Cage and Where No Man Has Gone Before comes out with a production design that isn't even remotely in line with either of those and is claiming to be in the same timeline. So no, it isn't. It is a visual reboot and more because the facts that they have put forward and the things they have put on the sets as Easter eggs counter so many points in the TOS timeline that there is no way it is not just a visual reboot but a total reboot. While it is sticking close to the original storyline, it is not letting the original stop any creative decisions they decide to make. They are paying lip-service to some fans who don't mind and totally blowing off those of us who have noticed and do mind. Frankly I really don't care what they do, but they need to stop pretending it is part of the original TOS timeline. They have made it clear it is not, both visually and factually. There is nothing about Discovery that can coexist with TOS.
Elsewhere on this site are deep and in depth discussions about the size of the TOS Enterprise and how you fit the sets inside with beautiful CG renderings of those sets inside the ships. There are hundreds of ways to tweak and update those sets and ships without totally revamping them. There are so many resources to stay on target with the original timeline and not throw in so many mistakes. The only explanation is that they don't want to follow that and that is what a reboot does. They pay homage to the original without copying it. That is what Discovery is doing (badly in season 1). But it is just as different a universe as we see in the Kelvin timeline. Where Enterprise fits I will not guess, but as far as TOS, the movies, TNG, DS9, and Voyager are concerned, Discovery is in a different timeline all together. What CBS or the producers say about it is irrelevant. Their decisions and actions have made it so.
So as far as I'm concerned there is the original timeline, the Kelvin original timeline, the Kelvin corrupted timeline, and the Discovery timeline. Enterprise can fit with any of them. The only one I consider truly Star Trek is the original.