Certainly when I was a student, I got the impression that my university saw its purpose as supporting research and training new researchers. One reason to like scholarships is that being a researcher doesn’t actually pay well so saddling people with lots of debt by graduation might discourage them from becoming researchers, though I’m not sure how much the university thought of that. It did feel like the majority of undergraduates who were not going to become researchers were a bit of an afterthought. However people outside had different ideas about what the university was trying to do, and the university obviously hoped to solicit donations from those students who eventually left.

The operating surplus is net of paying staff. If they increased their pay, wouldn’t it be lower?

But that’s the point: Harvard literally isn’t a “business enterprise under capitalism”. It’s a non-profit organization with no shareholders. Nobody has equity in Harvard.

Businesses tend to distribute their profits to shareholders, either through dividends or buybacks. Boards try to structure the way businesses are governed to align the interests of management with those of shareholders. But Harvard has no shareholders, so I’m not sure what you’re trying to suggest.