He would probably be more conflicted. On one hand, he would have the potential for great good, like the original Harry. But on the other hand, he would have the shadow of Bellatrix's dark deeds hanging over him. This internal conflict could make him more withdrawn at times. He might also have a fascination with the dark arts, not in an evil way, but more out of a need to understand his mother's world. This would set him apart from the Harry we know, who was always more firmly on the side of light magic.
It could be stronger in certain dark arts. Given his parentage, he might have a natural affinity for curses and hexes that are associated with the dark side. He could learn and perform these spells with greater ease compared to other wizards. However, he might struggle with defensive and positive magic, like healing spells or protective charms.
Bellatrix's character would have to be rewritten to some extent. Saving Harry would go against everything she has stood for in the original story. So, she might become more conflicted, showing both her old, evil self and a new, emerging self that is capable of good. Her relationships with other Death Eaters would also be affected, as they would view her actions as betrayal. This would add a whole new layer of drama and complexity to her character in the fanfic.
He might be more feral. Growing up with a monster, he could lack some of the social graces that a normal upbringing in the wizarding world would provide. He may be more direct and less concerned with propriety.
He might be more laid - back. Canadian culture is often seen as more relaxed, so Harry could have a calmer demeanor. He wouldn't be as quick to get into arguments or be as impulsive as he sometimes was in the original story.
Harry could become more secretive and distrustful. Growing up with Bellatrix, who is part of the Death Eaters and has a lot of secrets, Harry would learn to keep things to himself. He may not trust others easily, even those who seem friendly, as he has been brought up in an environment full of lies and hidden agendas.
Harry might be more confident in his pure - blood heritage. Since Dorea Black would likely educate him about it, he wouldn't feel as out of place among the pure - blood families as he did in the original story. He may carry himself with more pride, but not in an arrogant way.
Harry might be more secretive. He'd have to hide any doubts or conflicting feelings he has about the dark path he's being led down. Bellatrix would not tolerate any signs of weakness or deviation from her plans. So, he'd become very good at hiding his true self, which would make his personality complex and full of contradictions.
The story would become much darker. Bellatrix is a symbol of pure evil in the Potter universe.
Perhaps the biggest plot twist would be Harry's view of the Death Eaters. Growing up with the knowledge that his mother was Bellatrix, he might have a more sympathetic view of some of them at first. He could believe that they were misled rather than inherently evil. This would lead him on a journey to try and reform some of the Death Eaters, which would put him at odds with both the Order and the remaining Death Eaters who don't want to change. It would also change the way we see the divide between good and evil in the wizarding world.
Voldemort would be a likely character to interact with Harry. Since Bellatrix was one of Voldemort's most loyal followers, he might take an interest in Harry as her son. He could either see Harry as a potential powerful ally or a threat depending on how his powers develop. Another character could be Draco Malfoy. Given the connection between the Malfoy family and the Death Eaters, Draco might have a complex relationship with Harry, perhaps initially seeing him as an equal in the dark magic world but later having doubts as Harry shows signs of not fully embracing the dark side.