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.
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.
Yes. In fanfiction, writers love to blend different fictional worlds and create unique scenarios. If Harry Potter was Klaus Mikaelson's son in a fanfic, it would bring about a whole new set of storylines. For example, how would Hogwarts react to a student with not only magic but also a vampire - werewolf heritage? How would Dumbledore deal with a student who has the complex and often dark nature of Klaus? And how would Harry's relationships with his friends, like Ron and Hermione, change in this new context?
If they were to meet in a fanfiction, Klaus might try to use Harry for his own ends, like getting access to the powerful magic in the wizarding world. Harry would resist this, and in the process, they would have many intense exchanges. However, over time, they could start to understand each other's worlds better. For example, Klaus could explain the complex politics among vampires to Harry, and Harry could introduce Klaus to the concept of house rivalries at Hogwarts. This mutual understanding could lead to a more amicable relationship.
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 He might be more withdrawn as he tries to come to terms with it.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.