I was really disappointed with his appearance in Lower Decks. Q is a larger-than-life antagonist, literally the most powerful entity in all of Star Trek. He's a comic character, I get it, but in Lower Decks he was treated as a nuisance and not a threat.
In TNG, when Q appeared, that was a once-a-season event that pulled up red flags for everybody. He was fascinated by Picard and the Enterprise, but I didn't get the impression that he ventured out much more beyond that (his appearances on DS9 and Voyager being natural progressions from them stumbling onto Vash and Quinn).
In Lower Decks, we are expected to believe that he has been pestering this minor ship and even its most minor crewmembers on a persistent basis. Maybe if the Cerritos was a flagship of the Federation, we could be more understandable. But they're explicitly not. So, that leads me to believe that he's been pestering thousands of starships and millions of crewmembers all across the Federation (and beyond). Which he can do, it's in his power, but it lessens the threat assessment and eventfulness of a Q appearance considerably.
I think Lower Decks made an error with his appearance in their search for good parody. I love the show, but that is one of the two major missteps I felt they made in their first season.
Alternatively, Q only messes around with the protagonists of the TV series, which is a fun fourth wall break that he does allude to occasionally, but tends to break the immersion on my end.
Q belongs on Picard, because he is intricately tied into Picard's journey and through the "never-ending trial". I really could've gone all of Lower Decks without seeing Q. Maybe another Q (or even Q Junior) who gets fascinated with Mariner. Or maybe he could be pestering Riker on the Titan in their upcoming second season. Or maybe a natural evolution of his trial on humanity if the Cerritos ran across something or someone of value to the Q (a la Vash).
