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.
Harry would be a very different character. Since Robert Baratheon was a king and known for his love of wine and women, Harry might have a more hedonistic side. However, he'd also have the sense of duty that comes with being a Baratheon. In the wizarding world, this could translate to him being more assertive in protecting his friends and Hogwarts. He might also be more politically savvy, using his Baratheon - like charm to get his way in the complex social hierarchy of the wizarding world.
One possible plot could be that Harry, as the son of Robert Baratheon, grows up in a world where the wizarding and non - wizarding realms are more intertwined. He might face challenges from both the magical politics and the power struggles of the Seven Kingdoms. Maybe he'd use his magic to help resolve some of the disputes in Westeros, all while dealing with the secrets of his dual heritage.
His abilities might be a blend of his ninja skills and the more 'mundane' skills expected of a noble in Westeros. For example, he could use his shadow clone jutsu to attend multiple court meetings at once, while also learning how to joust or fight with a sword like a true Baratheon.
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.
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 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 He might be more withdrawn as he tries to come to terms with it.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 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 might be more self - reflective. Since Edmund had his own character arc of learning from his mistakes, Harry could inherit that trait. He would be quicker to admit when he's wrong and more likely to learn from his experiences.
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.
He would be more physically capable. Instead of just relying on magic, he could use his Wakandan - trained combat skills. His confidence might also be different. Growing up in Wakanda could give him a stronger sense of self - worth and a more regal bearing, which would set him apart from the original Harry Potter.