Maybe some of the Hogwarts professors could be involved. For example, Professor McGonagall could be concerned about Harry's new situation and offer her guidance. There could also be some descendants of previous island owners or caretakers who have their own interests in the island. They could either be friends or foes to Harry, adding more complexity to the story. Additionally, some magical creatures native to the island could be almost like characters themselves, interacting with Harry in unique ways.
Neville could be in it too. He might be initially shocked to see Harry in such a state but then tries to help by using some of his herbology knowledge to make a potion to counteract the drunkenness. And Malfoy could show up, taking the opportunity to mock Harry until Harry, in his drunken craziness, does something that scares Malfoy off. Also, Hagrid would surely be around, being concerned about Harry and trying to get him to rest in his hut.
Obviously, Harry himself is the central character. Then there could be his friends like Hermione and Ron. Hermione might help Harry manage his fortune in a smart way, like investing in magical books or rare potion ingredients. Ron could be the one who gives Harry more down - to - earth advice on how not to let the fortune change him.
Hermione would probably be involved. She could help Harry research about the island, like its history and any magical properties it might have.
One possible plot could be that Harry discovers the island is a magical place filled with ancient spells and potions. He might use it as a sanctuary away from the wizarding world's chaos, perhaps to study magic in peace and develop new spells.
In this fanfiction, the island could be a place where Harry's family had some sort of connection in the past. There could be a hidden family legacy there. Harry might find old family artifacts, and through exploring the island, he uncovers more about his family's history and how it ties into the wizarding world as a whole.
Hermione would surely be involved. She could be Harry's research partner, helping him find relevant medical information in books and scrolls. Her intelligence and thirst for knowledge would be very useful in exploring new areas of medical magic. Another character could be Madam Pomfrey. She could be Harry's mentor, teaching him the basics of wizarding medicine and guiding him in his new role as a medic.
Hermione could be involved. She might follow Harry through time to try and stop him from becoming the Dark Lord or to fix the timeline if he already has. Dumbledore is another character. In the past, he could sense something strange about Harry's presence and try to guide him away from the dark path. Young Tom Riddle would definitely be involved. He could be either an ally or an adversary to Harry, depending on the plot. Maybe he sees Harry as a kindred spirit or as a threat to his own rise to power.
Hermione could be a main character. She would probably be very involved in helping Harry with the baby, using her vast knowledge of magic to ensure the baby's well - being.
The supreme Mugwump himself could be a main character. He might have his own backstory, motives, and goals that drive the story forward.
One possible main character could be a Martian elder who takes Harry Potter under their wing and helps raise him. This Martian elder could have special knowledge about the planet and its hidden magic that they pass on to Harry.