File this under the "things you never thought you'd hear in Star Trek" category, but Ronald Moore, a writer for Star Trek: The Next Generation said Q (John de Lancie) was in love with Captain Picard (Patrick Stewart). That was one of the many reasons why Q had this fascination with the captain that he never had with anyone else in the Star Trek universe. And that much was obvious.
Q returned to Picard time and again, even returning in Star Trek: Picard season two when he was dying. At the end of the season, Q and Picard shared a hug, one of those "things you never thought you'd see in Star Trek." And there seemed to be genuine affection, and it's something Moore believed all along as he said in the companion book to the documentary series of the same name,The Center Seat - 55 Years of Trekby Peter Holmstrom [ via Screenrant].
"Internally, what we said all the time was Q is in love with Picard. That was the fundamental of the relationship. He’s in love with him. He just is. He loves Picard. It’s a particular relationship with this one human in this omnipotent being that’s bizarre, but that’s really what’s at the heart of it. Which is why, in my opinion, when they tried to translate him to Deep Space Nine and have a relationship with Sisko, it didn’t work because it didn’t, absent that element. Then Q just became a weird prankster that showed up arbitrarily, just to kind of screw with people. But with Picard, that was something personal. He had a personal relationship with this man, testing him, challenging him, protecting him. It was like a whole different kind of thing. And it just didn’t work with anybody else."- Ronald Moore
So was Q's return at the end of season three of Picard yet another way of getting the admiral's attention? Perhaps the being wasn't quite ready to let go of the relationship of sorts that he'd developed with Picard, no matter how dysfunctional it appeared to be onscreen. Inserting himself in Jack Crusher's (Ed Speleers) life would help him maintain the connection he had with Picard. Whatever the case may be, we won't see more unless Picard gets the Star Trek: Legacy spinoff that was set up in the finale.