His physical abilities would change drastically. He'd be much stronger and faster. No more getting winded while playing Quidditch. He could probably just fly around the pitch without a broom. And in duels, he could use his Saiyan strength to overpower opponents more easily.
His relationships would also be affected. Hermione might be constantly studying his Saiyan abilities and trying to figure out how they work with magic. Ron would probably be both jealous and in awe. And when it comes to facing Voldemort, Harry would approach the battle in a whole new way. He wouldn't just rely on spells like Expelliarmus, but also his super - punches and energy blasts. This would make the fight scenes in the story much more epic and different from the original Harry Potter series.
Harry would have a different upbringing. Maybe instead of just learning magic from the Dursleys' cupboard, he'd be doing some basic training like Goku did as a kid. His understanding of power would be different. He'd know that there's more to strength than just magic. And he might be more confident in himself because of his Saiyan heritage.
He'd probably have a hard time fitting in his dormitory. I mean, he might be too big for the bed! Also, Quidditch would be a whole new ball game. He could accidentally destroy the brooms or the goalposts with his strength. And the other students would likely be either in awe or terrified of him.
Harry's social circle would expand greatly. He'd be part of the Stark family and meet many influential people in the muggle world. At the same time, he'd still have his Hogwarts friends. This would create an interesting mix. He could introduce his wizard friends to things like video games and they could introduce him to new spells. His view of the world would be more inclusive of both magic and technology.
In this fanfiction, Harry's life at Hogwarts would be full of new discoveries. He could find secret passages that are overgrown with plants but are only visible to him because of his connection to Demeter. His friends might be a bit in awe of his new powers. He'd also have to deal with some jealousy from other students who don't have such unique abilities. And when it comes to Quidditch, he could use his nature powers to his advantage, like creating a gentle breeze to help him fly faster or making the grass on the pitch grow in a way that confounds his opponents.
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 powerful. Harry would likely have a sense of grandeur and a different view of his place in the world. His confidence might soar as he realizes he has such a powerful lineage.
His life would change drastically. He'd be in a world with different rules. No more wands perhaps, but instead ninja tools. His friends would be ninjas. He'd have to learn to move silently and quickly like a ninja.
His life would change drastically. He'd no longer be bullied by the Dursleys. Instead, he'd grow up in a more wild and free environment. He might be more in tune with his instincts.
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 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.