In this fanfiction, Harry might come across Tom Riddle before he fully became Voldemort. He could try to influence Tom in a positive way, to prevent him from turning to the dark side. He would also interact with other students from different generations. Maybe he'd befriend some students who were bullied or left out in the original timeline. And he would surely meet the house - elves of that time, and perhaps try to improve their living conditions much earlier than in his own time.
Obviously, he would interact with his parents, James and Lily. He could also meet a young Snape and try to change their relationship for the better. Dumbledore in his younger days would be another character. Harry might seek his advice or try to understand his earlier actions. Hagrid as a young gamekeeper would also be someone Harry would likely cross paths with.
Definitely his professors when they were younger. For example, Snape as a student. This would be a strange interaction considering their relationship in Harry's own time. He could also meet Hagrid when he was just starting out at Hogwarts. And there's a good chance he'd run into Sirius and Remus during their school days, and perhaps form new friendships or alliances with them in the past.
One character that would surely interact with Harry is Hagrid. Hagrid is always there for Harry in the main series, and in the fanfiction of traveling through books, he could introduce Harry to new magical creatures that are relevant to the specific book he has traveled into. Luna Lovegood could also be part of it. Her unique perspective on magic and the world could help Harry see things in a different light as he navigates through the different book - based scenarios. And then there's Ginny. Ginny, being Harry's love interest in the original series, would likely play an important role in the fanfiction, perhaps being involved in some of the adventures Harry has while traveling through the books.
The wizard Gandalf would be an obvious character for Harry to interact with. They are both wizards, though from different worlds. They could share their knowledge of magic, and Gandalf could guide Harry in the ways of Middle Earth while Harry could introduce some new magical concepts to Gandalf.
He might also interact with characters that are no longer alive in his present time. For example, an older werewolf or a witch who was powerful in the past. These interactions could provide Stiles with valuable knowledge or magic that he can use to his advantage when he returns to his own time. It could also create some really cool action scenes and moments of discovery as he uncovers secrets long forgotten.
Hermione is another common character. Since she is always so intelligent and resourceful, Harry might turn to her for help in understanding the implications of time travel. They could work together to change certain events, like preventing the release of some dark magic that they later had to face. And of course, Ron would also be around. His loyalty and friendship would be a source of support for Harry as he navigates this new timeline.
Ron and Hermione are very likely to interact with Harry. They are his closest friends in the original series, so in the fanfiction, they would still be important characters in his life. They might be in awe of his new all - powerful abilities or they could also be worried about how the power is changing him.
Obviously, he would interact with his father, James Potter. They could form a bond that Harry never had the chance to have in his own time. He would also meet Sirius Black, Remus Lupin, and Peter Pettigrew, the other Marauders.
He might interact with Luna Lovegood. She's always open to new and interesting conversations, and she could approach Harry when she sees him alone.
One possible plot could be that Harry goes back in time and tries to prevent certain tragedies from happening in the wizarding world. For example, he might try to stop Voldemort's rise to power much earlier. Another could be that he uses his knowledge of the future to improve relationships, like mending his friendship with Snape before it turned so sour. Maybe he also goes back to learn more about his parents and their time at Hogwarts.
Hermione is usually one of the main characters that interact with Harry. She might be in awe of his new powers at first but then help him use them wisely. Ron could also be there, perhaps being a bit more skeptical at the start but eventually coming around. Dumbledore might also play a role, guiding Harry even in his god - like state, sharing some of his own deep knowledge of magic.