I’ve worked for a university before and it was very common for staff to remote into their systems from home – usually with SSH for CS types or Remote Desktop/Team Viewer/etc. for less computer-focused folks. (The former usually didn’t have much issue – the folks using the latter mechanisms got compromised a number of times… -.-) There was also a campus provided VPN that was required to access certain systems with instructions to students and staff on how to use it, but other systems just got public IP addresses.

If what you’re doing is related to your work and campus IT doesn’t object, you’re probably fine to do it. I’ve run various kinds of websites and web apps for colleagues to collaborate on research projects. Being able to do things like that is kind of the point of the internet.

Having seen a number of students, uh, push the limits and find the boundaries of acceptability the hard way though… I’d strongly advise you not to install cryptominers, run TOR exit nodes, or torrent TV shows/movies/etc. That kind of thing tends to get your systems in hot water with IT or other parts of the bureaucracy…