SNW has a Lower Decks crossover episode, which is hilarious. Imo, SNW is essentially the only good characters taken from Discovery (which is fucking awful) and put in a far superior Trek. It’s got the same “doesn’t take itself too seriously while still addressing serious things” as some of the light-hearted Voyager/DS9 episodes.
That’s because SNW is traditional episodic Star Trek whereas Discovery and Picard are serialized series’s. Serialized series’s need to constantly escalate the tension and threats so you tend to get super serious action drama. Meanwhile, episodic series’s can get away with doing stuff like “how would the crew react to the entire ship turning pink?”
They both have their place in television, but Star Trek better lends itself to episodic format where you can have breaks to reset the tension.