and I don't see any value in limiting classification to the domain level. How would one classify wikipedia.org in this scenario? Would it not make more sense to define an open standard that'd leverage this system but allow domain managers to define it themselves?

To take my university.tld as the example, that university might host a file called at https://university.tld/ocs.json that looks something like this:

{
  "/": "EDU"
  "/math": "MAT",
  "/journalism": "JOU",
}

(Heads up to OP: there's no journalism in your current spec. That feels like an oversight.)

This would allow the high-content site admins to classify parts of the site differently. The /ocs.json file might even be dynamically generated for complex sites like Wikipedia.