If you feel that DS9 is recognizable but the newer series are not, then I ask you: What is it about the newer series that makes them unrecognizable? What fundamentally changed between the newer series and the older series?
I don't think DS9 from S4~ onward is recognisable, I think it feels like a generic WW2-in-space military sci-fi series that just uses Star Trek iconography in very thin ways. I would agree with you that people who consider DS9 "true Trek" but trash DSC/PIC might have a tough time explaining the distinction, though I'm sure people could come up with something.
Why does Star Trek have to "mean" anything? Why can't it just be entertaining and sometimes thought-provoking (not that the two are exclusive!) stories that take place in a shared multiverse?
You can say this about anything, but surely the point of a creative endeavour is to have some kind of unique selling point or distinct attributes.
If I put on an episode of "Murder, She Wrote", I'm going to get Jessica Fletcher solving a mystery. If I put on an episode of "Seinfeld", I'm going to get a certain comedy style with a consistent group of characters. If I put on an episode of "Mission: Impossible", I'm going to get Barney fiddling with a remote control for 30 minutes while Peter Graves tricks a dictator into thinking he's his own mother or something.
If I put on a production with "Star Trek" written on it, there's no consistent tone, characters, format, theme, premise, or even setting at this point since we're cut across four different centuries which all have no consistency anyway. It's just anything. It could be a 3-minute show aimed at toddlers or it could be a gritty prestige drama. It may not even be set in space. That's not a sign of a franchise in good health, IMO. I think even people who genuinely enjoy everything that's had the Star Trek name on it would have to agree that it's impossible to define what the title actually represents at this point, as I think you tacitly did there.
I'd also go at it from another angle and suggest that, in addition to Star Trek being eroded by so many conflicting and unrelated productions, it's a millstone around the neck of anything it's tied to, too. Discovery might have succeeded better on a creative level if almost everything was the same but it just wasn't called Star Trek, and thus didn't have to deal with the baggage.