His magic might be more aggressive. Growing up with the Dark Lord, he would be taught to use magic for more forceful and often cruel means. For instance, instead of using a simple Stunning Spell like in the original, he could be using more dangerous and unforgivable - like spells without hesitation.
His magic would probably be more esoteric. Since Zelretch has knowledge of different kinds of magic, Harry could learn spells or abilities that are not part of the normal Hogwarts curriculum. He might be able to manipulate time or space in ways that other wizards can't.
His magic could be more combat - oriented. Jiraiya's ninja background would likely influence Harry to use magic in a more direct and aggressive way in battles, rather than just for defensive or utility purposes like in the original series.
Harry's magic could be stronger. Dorea's influence and knowledge of magic could have allowed Harry to tap into his magic potential more easily. Maybe he would be able to perform advanced spells earlier. Also, his magic might have a different 'flavor' so to speak. Since Dorea comes from a different magical background than the Dursleys, Harry's magic could be more attuned to the traditional wizarding ways of magic use.
Well, in this fanfiction scenario, Fem Harry Potter's magic would be distinctively different. Since Poison Ivy has a strong connection with plants, Harry would be taught to harness the power of plants for her magic. She may not rely as much on incantations as in the original story. Instead, she could simply touch a plant and transfer her magic into it to make it do her bidding. Her magic would be less about structured spells from books and more about the instinctive connection with nature. For instance, she could make a flower bloom instantly and use the pollen to blind an opponent or create a path of growing plants to reach a high place instead of using a levitation spell.
Harry would likely be more wild in a sense. Dragons live by their instincts, and he'd pick up on that. His magical abilities could be more primal. Instead of relying on the spells taught in Hogwarts, he might use magic in a more raw and unrefined way. Also, his sense of loyalty might be more towards the dragons rather than the wizarding community initially.
His personality would probably be more aloof. Since basilisks are solitary creatures, Harry might not be as sociable as in the original story.
He would be more refined. Royal upbringing would instill in him a sense of propriety and elegance that he lacks in the original story.
Harry might have an easier time with spells related to transformation. Just as Poseidon can change the form of water, Harry could be more adept at transfiguration spells. He could also have a natural ability to breathe underwater and perform magic while submerged, which would be a huge advantage in certain situations. This would open up new possibilities for him in both the wizarding world and any underwater adventures he might have.
Harry's relationship with his family would be completely reimagined. Instead of having memories of his parents from the wizarding world, his sense of family would be centered around Gaara. He would have loyalty to Gaara in a way that is different from the traditional family bonds in the Harry Potter series. When he discovers his true heritage in the wizarding world, he might struggle to reconcile his newfound family connections with his loyalty to Gaara. This could lead to a complex and interesting exploration of family, loyalty, and identity in the fanfiction.
Harry would likely be more fearless and brash. Kenpachi is a bold and fearless fighter, and his influence would make Harry less hesitant. For example, when facing a bully like Draco, Harry might immediately react with physical force rather than just trading barbs. He would be more upfront and direct in his approach to problems.