One of his friends could be a young werewolf who is struggling to control his condition. Harry, having faced his own challenges, would befriend him and help him find a way to live a more normal life in the wizarding world.
One possible storyline could be Harry making friends with students from different houses at Hogwarts. For example, he befriends a shy Ravenclaw who helps him with his studies in a unique way. Another could be Harry befriending magical creatures, like a friendly centaur who gives him advice on dealing with the Forbidden Forest.
Harry Potter's friends in fanfiction vary a great deal. There are the international friends. Since Hogwarts is a British school but the wizarding world is global, in fanfiction, he could have friends from other magical schools around the world. These friends would bring in different magical cultures and techniques. Also, there are the friends who are from different time periods. Some fanfictions might introduce time - travel elements, and Harry could befriend wizards or witches from the past or future. His relationships with these friends can be complex, as they have different values and ways of life based on their time of origin.
It could be that he is wrongly perceived as dangerous. After all, he has survived the Killing Curse as a baby and Voldemort is always after him. People might be afraid to get close to him for fear of getting caught up in the dark wizard's wrath.
It could be a mysterious stranger. Maybe someone who has been observing Harry from afar and decides that he needs a different wand for some greater purpose. This stranger might have their own motives, perhaps related to a prophecy or a hidden plan within the wizarding world.
Harry could try to change his appearance or behavior slightly if they are the things that make others avoid him. But more importantly, he should communicate his true self to others. He can share his stories, dreams, and fears. This vulnerability can make others feel closer to him. He might also need to seek out those who are more accepting and open - minded. Maybe there are some outcasts or loners like him in the fanfiction world, and they can form a group together first and then gradually expand their social circle.
He might focus on his studies. In the wizarding world, there are so many interesting magical subjects like Potions, Transfiguration. By burying himself in books and learning new spells, he can at least distract himself from the lack of friends.
Byakuran might have some unique powers from his own world. His powers could be used to create diversions or solve certain physical challenges. Luna, with her perceptive and dreamy nature, can often see things others miss. She can sense hidden motives or spot secret passages. Harry, of course, has his magical skills from Hogwarts like his proficiency in spells. His ability to fight dark magic is crucial. So, Byakuran's physical power skills, Luna's perceptive skills, and Harry's combat magic skills work together well. For example, when facing a dangerous enemy, Byakuran can hold it off physically, Luna can figure out its weak points, and Harry can then use a spell to defeat it.