Prequel to TMP. I think DSC doesn't mesh too bad with the TOS Movies. The design for the Discovery itself actually comes from the
unused design for
Planet of the Titans, an undeveloped Star Trek movie in the '70s, back when they were volley-balling between the idea of whether or not Star Trek would come back as a TV series or a movie. The black and dark-blue computer graphics fit right into Post-TUC. If they'd set this show in the Early-24th Century, it would look seamless.
The moment I saw the look of DSC in the first preview, I thought, "visually, this can't line up". So I disregarded the idea immediately. Someone tried to come up with some bullshit explanation or rationale for how it all visually fit together, when I came to this conclusion to 2017, and I dismissed it on the spot one time and had to shut someone else up another time. I think of DSC's first two seasons and SNW as leading into some hypothetical version of TOS with modern production values. Anyway, I think those two people I just mentioned thought I was going to hate the show, until they realized better, and then no one bothered me about it. You don't piss off one of the people who's defending the show the hardest, after all.
When I see the Enterprise in DSC, I don't think "this leads into actual TOS". I call a spade a spade. It's three timelines. CBS says it's Prime, so I call TOS something else. Classic. It's just a name.
I know they said it all fits together. But I listen to PR from Studios the same way I listen to PR from Politicians and their staff. I listen to it the same way I listened to Rick Berman's "We're very pleased." I make my own judgments and decide for myself.
I think people tend to look the other way if they like something. I didn't like ENT, so I didn't look the other way. I like DSC, so I thought, "It's three timelines" and called it a day.