They do. They also own lots of intellectual property and will provide some amount of financial support to startups that grow out of the university commonly. At the end of the day, they have endowments and they want to grow those.

Specifically, regarding property, at schools I’ve attended they owned real estate in the city around the campus, not just the campus itself. Part of that is investment and part of it was looking to the future for when they run out of space on the current campus to build new facilities and need to grow the campus

We don’t think of pension funds as hedge funds either but they also invest heavily to grow the fund.

Which universities in Australia? Most of the student accommodation is independent (especially ones associated with the sandstone unis, see https://www.abc.net.au/triplej/programs/hack/broderick-revie... for why that's sometimes a problem), and there's no requirement to use student accommodation. International student tuition is a major funding source, but I've never heard of accommodation being much of a money spinner.