Broberg's easier and faster path to the NHL was removed when the Oilers acquired Ekholm, which we all agree was a great acquisition. One could argue that then onus was on management to move Kulak to create a spot during the 2023-24 season, but Broberg's underwhelming camp, the early season tail spin and eventual recovery probably had management wanting run with a veteran in Kulak down the stretch and through the playoffs.
While Broberg played in Bakersfield all season, his agent used the situation to get him ready to pursue opportunities outside the Oilers, so I imagine Broberg re-signing was unlikely. He received the offer sheet he wanted and now he's a Blues player.