He reacts fairly normally for someone who has suffered the sort of abuse he has
Harry being physically abused by the Dursleys is largely fan-canon. Instead, they provide the bare necessities of life to him, and deprive him of positive emotional interaction. We see this reflect in Harry's actions in the book, where he's grateful for everything he has, even extremely mundane things like as much food as he cares to eat, or a comfortable bed. He does not innately feel he deserves these things, so he stays grateful. Similarly, he treasures his interactions with others, and is constantly trying to find ways to make them happy since they've made him so happy, and he makes friends with pretty much anyone who doesn't push him away. Lastly, because the closest to success he's managed for positive interactions with adults in his life is by being polite and proper and quiet, that's how he deals with the adults in his life. He treats most of his professors with respect, and he doesn't bother them with his troubles, because he knows that adults, even when given the truth, will never step in for him.
Lastly, he shows a disregard for his own safety and an unhealthy desire to be useful to the people around him. As with his politeness to other adults, Harry likely got the closest to approval from the Dursleys for being useful whether it was doing chores or being their emotional punching bag. And, well, he's probably more than a bit conditioned to the idea that disobeying orders from an adult can lead to punishment, so he barely even questions his role as the Chosen One, accepting that role and performing to his best ability.
Some aspects probably are abnormal, but might just a matter of his personal reaction
Realistically, I'd argue that Harry ought to show some negative traits that do not show up in the books. For example, having seldom received more than adequate food from his family, I'm surprised there's not more food hoarding going on. We do see a bit of it with how he splurges on the sweets from the trolley, but I think that was in part because he wanted to get them for Ron. As someone who has likely gone hungry any time he was locked in his closet without dinner, I would have expected him to be sneaking food off of the table in the Hall, caching candy, etc.
Also, Harry takes people at face value more than I would expect from someone who grew up in an emotionally abusive household. He doesn't look for ulterior motives, or assume that people are only being nice to him in preparation to betray him. While, as others note in the comments, he can have a bit of a temper, he seldom just lashes out at people, or freezes them out.
But, in the end, it might just be who he is
Ultimately, though, people react to trauma in different ways, and he may have had more positive models in the people he interacted with outside of the Dursleys. He may have recognized, if only subconsciously, that the Dursleys were outliers, and he's built his identity and belief in how people ought to interact by viewing others, whether in real life or via popular media. We also don't know exactly when the Dursleys became so cold to him. It could be that, in his early years, they did treat him as lost family, and it was only later, as feats of accidental magic occurred, the Dursleys started getting more weird interactions with Wizarding folk approaching Harry on the street, and Harry started to look more like his parents, that they turned on him.
And, well, it's a children's book and they often gloss over the negative effects of childhood neglect. Hansel and Gretel didn't show signs of trauma. Cinderella didn't show signs of trauma. Little Orphan Annie is a constant ray of sunshine. It's not realistic, but maybe the realism is not necessary.
