But was it a "new" version in this case?
Yes, obviously, in every way that matters -- new stories, new cast, new look, new attitude. The in-universe continuity ties are just a handwave to make a massive reinterpretation palatable to old-guard fans. In real-world terms, looking at it as an exercise in storytelling and marketing, the express intent was to make
Star Trek new, to relaunch the film franchise in a fresh way that would attract a fresh young audience. You can't make a profit by catering solely to old fans, since that's a population that's bound to dwindle over time. You have to periodically start over and appeal to new audiences, people who never saw the old version. So when you do that, there's no requirement to make it continuous with what came before, because it won't matter either way to the new audience. That's an option, but it's a secondary consideration. As I keep saying, continuity is not the sole purpose of fiction or the sole standard for judging fiction.
And there are different kinds of continuity. Clearly the Marvel Cinematic Universe and the Arrowverse are not in the same continuity as the comics they're based on, but they've been very good at respecting and adapting the characters and storylines and worldbuilding elements of their sources,
using past continuity as a starting point and a font to draw from rather than being confined by it. Continuity of
ideas, characters, and themes is more important to fiction than the literalistic continuity of events and chronology. You don't have to set your story in the same "universe" as an earlier one in order to be faithful and respectful to its essence.
But remember that a lot of the older inconsistencies were simply due to technical issues, primarily a lack of easily-accessible reference (especially wikis), and some of them could also pass unnoticed for the same reason, so it’s only a natural evolution that now we’d be less accepting of those in absence of a formal handwave (eg. “reboot”, “alternate universe”, “timeline reset”).
Up to a point, but as with anything else, it becomes harmful when it's taken to a fundamentalist extreme. I've always been obsessive about continuity details myself. It's my first impulse. But your first impulse in a place from which to start thinking, not to stop thinking. I have enough perspective and experience to recognize that it's not the sole consideration that matters, that it's one tool out of many that different creators are entitled to wield in different ways, and that there can be good and necessary reasons for prioritizing other things above it. Life is too complicated to judge everything by a single yardstick.