I used to view Star Trek as where the main story was about the Enterprise. TOS was the Original, TNG was the Sequel, ENT was the Prequel, and then DS9, VOY, and DSC were all spin-offs based on the Star Trek Universe.
So, if you treat the main story of Star Trek as being on the Enterprise, then Picard is a Star Trek Spin-Off. But, if you look at TNG in and of itself, and Picard is the lead character, then Picard is a sequel to that character's life and a sequel to what was started in TNG.
So, I think Picard is both: a Star Trek Spin-Off and a TNG Sequel at the same time. In the case of it being a TNG Sequel, it's like going from Alien to Aliens. You still have Ripley, but she's with another crew and she's carried her experiences from the previous installment with her.
I would just say that I don't think Star Trek has a "main story." I would argue that Star Trek is a collection of stories, not a unified story in and of itself; a setting, not a saga. Star Trek is not Star Wars or Battlestar Galactica or Babylon 5 or Firefly in that regard.