I think someone needs to look up how to define a spin-off. "A spin-off in television is a new series containing characters or settings that originated in a previous series, but with a different focus, tone, or theme." By that definition alone, Strange New Worlds and Section 31, and by a long extension, Lower Decks, are the only spin-offs of Discovery. This makes Discovery's spin-off count 3. And that is being generous because Lower Decks is only a spin-off of Discovery because of one episode that includes cast and characters from Strange New Worlds, a spin-off of Discovery.

And by the previously mentioned definition, Picard and Lower Decks are spin-offs of TNG and Prodigy is a spin-off of Voyager. Lower Decks is directly a spin-off of TNG because the two shows share characters and actors, and not through another show. While one can argue that Voyager is only a distant spin-off TNG, TNG still has Enterprise, DS9, Picard, and Lower Decks. That makes the count 4 to 3 in favor of TNG.

Discovery is a good show (season 3 onward), but it is in no way the ground breaking show that some seem to think it is. It is not the first trek show helmed by a non-captain, an African American, or have a homosexual relationship (DS9 had all three [although Jadzia was not lesbian, she still had the first homosexual relationship]). The only firsts that Discovery had were the first openly homosexual couple and the first live-action show to not make more than 70 episodes, making it the shortest Star Trek live-action series by number of episodes when it ended. And while Jadzia had a homosexual relationship on DS9, it's hard to argue that it was "openly" homosexual because the two characters were married when one was previously a man and the other was a woman and in their current incarnations, the characters had to keep their relationship a secret. But then you could argue that DS9 had the first transgender character in Jadzia.