I used to think like that and still think none of it really fits, but when you watch an episode of Discovery and they're literally watching clips of TNG episodes in it, or using TOS clips in "previously on..." segments it's hard to deny their intent is 100% that they're the same fictional world.Yes. It is their interpretation of what is going on. Whether anyone likes it or not, Discovery was made 54 years after the original Star Trek. From my point of view, there is simply no way they can occur concurrently in the same universe. We are simply too different in what we believe, our general experiences too different from the creators of five decades ago.
From CBS point of view, calling it “Prime” is a calculated business decision, designed to pacify fans who can’t or won’t let go of the past
When discussing 23rd century stuff you have to specify whether you're talking about the TOS, AOS or DSC versions of it because they are all different people IRL putting different spins on it. But they're all intended as the same fictional world.