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.
His status would be much different. He'd likely be seen as even more special. The other students might either be in awe or jealous. Teachers might also treat him differently, expecting more from him in terms of leadership and courage.
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.
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.
In terms of his classes, Defense Against the Dark Arts would be a whole new experience. He could use his Saiyan powers to counter dark magic in ways that no one has ever seen before. He might even develop his own unique spells that are a blend of magic and Saiyan energy, making him a truly formidable wizard - Saiyan hybrid at Hogwarts.
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'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.
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.
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.