Honestly, I been on Tiktok (please don't criticize me base on that alone) and found a video mocking how Harry had a fortune that he didn't share with the Weasley. I pointed out he was not that rich and someone say he is just as rich as Draco family.
Now, I read the book so I know that Molly and Arthur would refused Harry offering his money. But in the third book, Harry clsim that he wished he could buy a firebolt... but he convince himself to save his money to get through the other four to five years in Hogwarts (plus some money for their food). When I point this out, they claim the firebolt must have been too expensive.
In the end of the argument, I am left wondering how rich is Harry given his parents fortune.
WHY • THESE • CRETINS • DO • NOT • READ • THE • FUCKING • BOOKS
Anyway. Post-books it has been explained that his grand-grandfather was a prominent Wizangamot member and his grandfather Fleamont invented the Sleekeazy's Potion (yes the mixture Hermione used for the Yule Ball), whose success quadrupled the family gold. When James was born, he sold the company making even more money and retired.
Considering
I'd say he's rich.