I summarize five obviously pro-liberty themes in the novels: their anti-tyranny story arch, the heroes’ opposition to slavery and oppression, the stories’ acknowledgement that power tends to corrupt, their portrayal of heroes boldly standing up to abusive power, and their portrayal of government at its best as protecting people from criminal harm.
Unsurprisingly, then, from the perspective of economic liberty or classical liberalism, several of the Potter themes are ambiguous regarding liberty. While there is no obvious welfare state in the wizard world, this may mean only that the government is not sufficiently advanced for that. The wizarding government maintains an ambitious regulatory state, controlling things from transportation to dragon breeding to cauldron thickness. Finally, the wizards enforce (limited) segregation from the non-magical Muggles, leading to more controls on wizards and Muggles alike.
Yet, on the whole, the novels are wonderfully pro-liberty, and that’s a big reason I love them so much.