So after watching through the entirety of DSC, ENT and VOY, I'm now re-watching TOS, and one thing really springs to mind. In TOS, they're more often than not confronted with someone or something that's beyond their own power or even understanding. It's often a humbling encounter that's resolved with tactics and wit, not by force or superior technology. That's what good Star Trek is to me, being confronted with something otherworldly beyond your comprehension.
I don't hate VOY, but it couldn't be more different. In most episodes, VOY encounters some single-episode throwaway alien jerks with inferior technology, and more often than not they have to succumb to Voyager's technology and holier-than-thou ethics.
The thing is, in VOY everything's trivialised. It struggled to make its own interesting aliens, then resorted to bringing back the Borg, and even the Borg were trivialised in the sense that they could be so easily outsmarted. The same Borg that were so overwhelming that Picard begged Q for help are hardly more than a nuisance here. Speaking of Q, he must ask Janeway for parenting advice in VOY, so even they are trivialised. And where Kirk had to be smart, VOY often just has to remodulate subspace harmonics or whatever shit just came to mind.
Another thing, this time mostly in contrast to ENT, is the Vulcans. For all the human self-importance on display in TOS, Spock is an extremely capable and important officer not despite, but because he's Vulcan. He's very good, very efficient, and Kirk doesn't seem to try to change him, because he knows very well how good Spock is. He takes him as he is. Here, the Vulcan is someone with flaws but whose approach and strengths are incredibly valuable. In ENT, Vulcans are most of the time depicted as stubborn idiots, and Archer constantly tries to assimilate poor T'Pol. In contrast to TOS, in ENT being Vulcan seems to be a flaw, a flaw that can be fixed by making them more human.
So, back to the question: what is Star Trek to me and what isn't? To me, Star Trek means reaching out to the universe and encountering things we're not prepared for, that are beyond our imagination. To me, it doesn't mean laser gun battles, reversing shield polarity, or out-teleporting the Klingon flagship.
And this is why TMP, for all its flaws, is still my favourite Trek movie.