There's a chance that Neville could stumble upon Harry's isolated place. Neville has always had a connection with Harry, and he might be worried about Harry living alone and come to check on him. Also, thestrals could play a role. Since they are associated with death and Harry has seen so much of it, they might be drawn to him and he could form a bond with them.
In some fanfictions, a mysterious old wizard living in the Forbidden Forest could interact with Harry. This wizard could be someone with great knowledge, perhaps a hermit who has been observing Harry from afar. And, of course, Hedwig could still be with Harry, providing not just a connection to the outside world but also being a source of comfort in his solitude.
One character could be Dobby. Even though Harry is living alone, Dobby might still find a way to visit him and offer his help. Another could be the Hogwarts ghosts. They can pass through walls and might visit Harry in his solitary abode.
A potential character could be a reclusive old wizard who lives on the outskirts of the wizarding world. This wizard might have his own reasons for living in seclusion, but when he sees Harry's loneliness, he takes him under his wing. Another character could be a young, orphaned witch who is also trying to find her place in the post - war wizarding world and she crosses paths with Harry.
Obviously, Buffy would be a major character he'd interact with. They could start off as wary of each other but then grow to respect one another's fighting skills. Giles too, as he has a wealth of knowledge about the supernatural, and he and Harry could have some interesting discussions about different types of magic.
Ron could also be involved. He might initially be a bit skeptical or jealous of the sister, but as they go through adventures together, they become friends. Maybe they get into some comical situations, like when they are trying to sneak into a restricted area of Hogwarts to find something related to the sister's forgotten past.
There could be forest animals like wise old owls or friendly squirrels that interact with him.
Obviously, Hagrid could be one. He would be so amazed and probably take baby Harry on little adventures around the Hogwarts grounds, listening intently to what Harry has to say.
There are many potential characters. The teachers at Forks High School for sure. Harry could have interesting conversations with them. Also, if there are any other supernatural beings in the Forks universe in this fanfiction, like werewolves, he could interact with them. And of course, the students who are into different clubs and activities at the school. He might bond with the science - loving students or those on the school newspaper team, sharing his own experiences from Hogwarts in a veiled way.
Alien races that are envious of the Earth - born magic could be enemies. They might see Harry and the wizards as a threat to their own power and dominance in the universe. Also, there could be dark wizards who have escaped to space to avoid the law on Earth and continue their evil deeds, now with a new set of space - related challenges and opportunities.
Definitely Sam and Dean Winchester. They would be like his surrogate brothers or mentors. Then there's Castiel, the angel. He could have some interesting interactions with Harry, perhaps being intrigued by his magic. Bobby Singer could also be there, guiding Harry in the ways of hunting.
He could meet an Egyptian wizard who is an expert in ancient magic. This wizard could teach Harry a great deal about the history of magic in Egypt.
A new coworker at Harry's muggle job could be introduced. This coworker might be really into conspiracy theories and start to suspect that Harry is something more than he seems. They could form an interesting dynamic as Harry tries to avoid the coworker's prying questions.