It seems this is mostly an Asian thing, where children and teenagers may get sent to so-called “tutorial centres” after school for more learning. Some think these tutorial centres are only to let their parents work longer hours, but that’s irrelevant in OSM.
What is relevant is that, it seems there is currently no way to tag these tutorial centres. These are clearly not education=school, but at the same time, they aren’t specialized schools like language schools. It seems they need a new tag.
Would “interest prep schools” count as education=prep_school? Like, drawing schools for children, often planned by parents to learn some side skills or something.
We have in Greece such centers aswell, called “φροντιστήρια”, usually offered for students of ages 14-18, and indeed “prep school” looks like the proper one.
Because there’s the “education” tag reformation going on which promotes the use of education=* for school-type amenities, per the wiki I would go for amenity=school and education=prep_school