building functions….

It works, but in my opinion "function" is a bit a of an overly generic word. It's a bit like the word "type". I think we should avoid those kinds of words as keys.

Some functions could maybe be better covered by existing tags. For example the canteen could perhaps be mapped as a restaurant (although if it's very private, then that might be poor fit) The careers centre is a lot like a job centre or employment agency, which we're missing decent tag documentation on unfortunately, but the point is you can map these things with "top-level" tags rather than using a generic word "function".

Another approach used by some mappers, is to represent some types/functions of buildings within the building tag. So instead of just building=yes, do building=catering or something. A bit weird but probably better than using a new "function" key.

I thought we had a page on the wiki about campus mapping, but maybe it was my imagination. So today I wrote a bunch more stuff on the Tag:amenity=unversity page, although I haven't actually answered your question. We could add more detail to the 'Detailed campus mapping' section (or this could go new 'University campuses' wiki page)