Jason Grace's lack of personality is an intentional choice on Rick's part to deconstruct what makes the "perfect hero" or the "ideal guy."
Jason's entire character revolves around having everything but still feeling incomplete. Being the golden child and still unfulfilled. Being revered by all but not intimately knowing anyone. No one really knows him.
He's never gotten to chose for himself. Juno plays with his life from day one. His name has already determined his fate. His future is set in stone and it isn't until the end of Heroes of Olympus he makes the choice to veer away from the path he was given - that of praetor, of hero, of the leader.
Jason is intriguing because of his relation to others. Thalia's brother. Nico's friend. Percy's foil. Piper's (comphet) boyfriend. He provides padding for others. His introduction into the universe is meant to help the reader feel Percy's absence. He was never meant to replace Percy, but he constantly feels like he has to.
Jason Grace, who forms connections with the people around him. Who inspires Hazel, befriends and protects Nico, supports Leo, aids Piper in her progression. Jason, who refuses to chose a single camp to stand with. Jason who is constantly held to perfection. Jason who carves his own path despite being consistently stripped of his humanity and agency.
Jason Grace, who died a hero.
