I think the confusion is that while the show producers have a canon timeline split, there is a visual and tone shift linked to the 09 films. We have 3 major branches at this point.
"Classic" Trek. TOS through Enterprise. Is pretty much dead except spiritually in The Orville series.
Abrams 09 reboot films.
Discovery and now Picard.
Classic Trek is mostly optimistic, with a dip into a bit of deconstruction (DS9 and some Enterprise) and a hard nose dive into action schlock during the TNG films.
Abrams 09 Trek is flashy mindless action nonsense, with a bit of a pull-up into Classic Trek with Beyond, but not enough to save the films.
Discovery Trek retains the flash and mindless action of the Abrams films, but is a hard turn into dystopia and aggressive violence. Picard is seeming to double down on this.
While these branches aren't due to any story elements, they are visually and tonally distinctive enough to make them different versions of Star Trek.