Wil Wheaton has offered his official answer to why Wesley Crusher is missing from Picard season 3. Though the final season of Picard was packed with appearances by returning Star Trek: The Next Generation actors, Wheaton's Wesley was a glaring absentee. That absence was amplified by the fact that Picard season 3 saw the introduction of Wesley's brother Jack Crusher (Ed Speeler).
While it is perhaps more dramatic to imagine that Wesley didn't return in Picard season 3 to visit his family over some old wounds, Wheaton's own head canon explanation is all the more tragic. According to the Big Bang Theory star and Star Trek aftershow host, Wesley's Picard season 3 absence was a necessity: the Traveler simply wasn't allowed to return, because of the sacrifice he made:
Wheaton took to Facebook to respond to a Gizmodo article on Picard's biggest unanswered questions, revealing Wesley has never met his brother and while he burns to visit his mother, he is forbidden because of his choice to give up his human life. He made that choice in "Journey's End," leaving Starfleet after clashing with their morality system, and seeking the higher path offered by The Traveler.