His loyalty would be more complex. While he's always been loyal to his friends in the original story, in this fanfiction, he might have to balance his loyalty to the wizarding world and his newfound family, the Mikaelsons. He might question where his true allegiances lie. His physical appearance could also change. He might have some of the alluring features of the Mikaelsons, which could attract different reactions from people around him, both positive and negative, and this would further shape his character.
He would probably be more confident. Since the Mikaelsons are known for their assertiveness, Harry might inherit some of that trait. He could be more bold in standing up to his enemies, not just Voldemort but also bullies at Hogwarts.
Harry would likely be more ruthless. Klaus has a reputation for being cruel when necessary, and Harry might have a bit of that in him. He may not hesitate as much to use more extreme measures against his enemies, like the Death Eaters. However, he would also have to struggle with this darker side of his nature, as he has been brought up in the relatively more morally - bound wizarding world. His friends like Hermione and Ron might be shocked at first by these new aspects of his personality, but they would also try to help him stay true to the good values he has learned at Hogwarts.
The plot might involve Harry trying to hide his true identity as a Mikaelson. He could struggle with the fact that he's different from other wizards. His relationship with his friends, like Hermione and Ron, could be strained as he tries to keep this secret. Also, the Mikaelson family might try to get him involved in their vampire world affairs, which would create a whole new set of challenges for Harry.
He would probably be more otherworldly. Harry might have an air of mystery around him that the original Harry didn't have. His actions could be more guided by a sense of divine purpose.
He would likely become more conflicted. Harry, who was always on the side of good, would now have to deal with this dark lineage. He might be more withdrawn as he tries to come to terms with it.
He would probably be more in tune with nature. Instead of just having a connection to Hedwig, he might be able to communicate with all kinds of animals. So he could be more of a naturalist wizard.
He would likely be more conflicted. Harry was always a morally upright character, but with Thanos as his father, he'd have to battle inner demons. He might be more powerful physically and have a darker side to his personality that he constantly has to keep in check.
He would be much more physically powerful. Instead of relying just on magic, he could use his Saiyan strength to solve problems. For instance, he might be able to break through magically locked doors with his bare hands.
Harry would likely have a different sense of self - worth. Knowing he is the son of a powerful underwater hero like Aquaman, he would carry himself with more pride. He might also be more in tune with his emotions, as the ocean is often associated with depth of feeling. And his magical abilities could be enhanced in ways related to water, like creating more powerful water - based spells. He could also be more of a loner, as his unique heritage might make it hard for others to fully understand him.
He would be more aggressive. As a Baratheon, he'd inherit that family's bold and sometimes brash nature. Instead of the somewhat reserved Harry we know, he'd be more likely to take immediate action, whether in a duel or in dealing with a problem at Hogwarts.
He might be more confident in dealing with non - magical people. Since Pepper is used to operating in a world full of normal humans, Harry could have a better understanding of how muggles think. Also, he might be more tech - savvy, using modern devices to aid his magic or to keep in touch with his wizarding friends in a different way.