It could potentially make Harry more empathetic towards others who are in fearful situations. Since he has experienced such intense fear himself, he may be more likely to understand and help those who are also afraid. In the fanfiction, this could be shown through his interactions with other characters who are facing their own fears.
Perhaps his uncle has a very intimidating appearance or a loud voice that scares Harry. In the fanfiction, it could be that his uncle has a certain look in his eyes when he's angry that makes Harry tremble with fear.
It can make him more independent. Without his parents' protection, Harry has to learn to fend for himself, which can lead to him becoming more self - reliant. He'll have to figure out how to solve problems on his own.
The neglect can lead to a sense of distrust in Harry towards family - like relationships. He might be more hesitant to form close bonds with others at first. However, as he grows, he learns to distinguish between those who truly care for him and those who don't. This experience also gives him a deep well of empathy for others who have been through similar situations, which shapes his character into a more understanding and kind person in the long run. He has to face many challenges alone, which toughens his mental state and makes him a more resilient wizard.
The fear could also make him question his own identity as a ninja. If he is afraid of ninjas, does that mean he is also afraid of what he is? This internal conflict would be a major part of his character development. He would have to face his fear, understand the true nature of being a ninja, and decide whether he wants to continue on the ninja path or find an alternative way of life.
If Harry is taller in fanfiction, it could make him seem more confident. People often associate height with leadership, so he might take on more of a leadership role among his peers.
He might be more distrustful. The feeling of being abandoned could make it hard for him to trust others easily. For example, when he first meets Dumbledore or his new friends at Hogwarts, he may be hesitant to open up completely because he's been let down by the most important people in his life - his parents.
Well, it likely makes him more independent. He has to rely on himself more without parental support. He might grow up quicker, learning to fend for himself and make his own decisions earlier than he would have with loving parents.
It makes him more brooding. Harry might become more withdrawn as he contemplates the 'death' within his scars. He could be constantly reminded of the fragility of life and the nearness of death, which would make him more cautious and less impulsive in his actions.
Well, it could make him more independent. Without the initial love and protection from his parents, Harry has to learn to fend for himself at a very young age. So when he gets to Hogwarts, he might be more likely to take risks and not rely on others as much.
It could make him more cautious. After talking to the Horcrux, he realizes how devious Voldemort's magic can be and becomes more careful in his future encounters with dark magic.