While I'm a huge fan of his, Bouchard is both having a down year and has never fixed his D-zone issues, as they are the same now as they were in the OHL. He likely tops out as a 2nd pair D and 1st PP QB, which still has considerable value.
Don't be fooled, a 6'4" athlete who can skate, grind along the wall, drive the net, and shoot the puck has value, Puljujarvi is still young and is in the process of learning that "the game is 100% mental". As a reclamation project and cap hit, he makes sense on both sides of the deal.
SJ has top young wing prospects, they can use the C more than Edmonton needs one, so Bourgault is an easy choice here. He makes more sense than the 2024 1st round pick, which if this goes well for Edmonton, would be a very late pick.
Barrie is not in this deal, as in the past few days it was reported that Edmonton thinks that he's been their best D this year, and they have no desire to move him. If you've followed his career, you also know that he's a top guy in the dressing room, so between on and off the ice, they have no reason to deal him.
This is an all-or-nothing trade that you only make if you think you can win the Stanley Cup this year, if not the next 2-3 years. If Karlsson stays at this level or even at a point per game, adding him to this team makes Edmonton a favourite for as long as Karlsson is elite.