Not entirely accurate. The KelvinVerse belongs to Paramount. That is why the Star Trek Novels do not feature the destruction of Romulus, Simon &Schuster/Pocket Books operate on a CBS license only. To my knowledge the only group operating on both a CBS, and Paramount license is Star Trek Online.
I think the IDW license covers both - but I seem to recall the IDW license doesn't cover DS9 or something like that?
They have the same parent company, so I'm not sure if it's completely out of the question if there could be some sort of agreement. But I actually like the idea of the TV and movie properties being separate 'universes'. That way they don't have to track each other and can just focus on delivering a good story.
My new theory... The Prime Universe has always looked the way it does on Discovery. Between Discovery and the Pike era, someone has meddled with the past (Guardian of Forever maybe?) resulting in the TOS look we all know and love. Only Guinan remembers the way it was
I used to try and rationalise and make sense of Trek's temporal shenanigans, but I realised the only way to accurately sum it up is thusly: