Is TNotW really the same concept as Harry Potter? It has a university in it, which I guess is similar to a school, and after a while the main character ends up there, but it's a very different concept - it's classic high fantasy that includes a period of learning and study, whereas HP is primarily boarding school fiction with magical elements. Similarly, The Magicians, as I understand it, is also more about a university, and is perhaps closer in lineage to Buffy or Charmed than to Harry Potter - it has more of that focus on the interpersonal relationships between characters, and a more complex morality.

The better comparison is probably with Percy Jackson, which isn't quite the same concept (being an American series, where boarding school fiction isn't quite as well-known a genre) but matches the ages, sense of discovery, and relationships to authority figures far better.

This isn't directly relevant to your point, but I really find it wild that people see two stories that have magic and a school in them and go "look, it's the same thing", especially when the genres and tropes of the two books are so utterly different. For that matter, Harry Potter is also nothing like Earthsea, which is another common reference point. I wonder if Americans just don't have as much experience with boarding school fiction to be able to categorise Harry Potter as a series?