Mac mini server A1347 can't use Wi-Fi during setup
There is no (reasonable) way around this. Basically, what's going on is that the firmware's network stack isn't smart enough to do 802.1X authentication (which is what's used for "enterprise" Wi-Fi authentication with both username and password). It can only do "personal" Wi-Fi authentication (network password, no username) an open networks (no captive portals either -- they require a browser). And ethernet, of course.

As for resharing the network (e.g. from your Mac) there's no technical reason this can't be done, but there's an extremely good practical one: 802.1X authentication implies a relatively high-security network, and particularly one where the network admins want to be able to tell who's connected where and when. Resharing such a network connection would open a hole in the network security, as well as potentially allowing untraceable and probably unauthorized people to connect to the network. From a security policy perspective, this would be very very bad. So macOS doesn't allow it.

Possible solutions: Can you get access to the campus network over ethernet? If so, you could use that (unless it also requires 802.1X authentication, but that's rare). If not, you're going to have to take the Mac Mini somewhere else to get an Internet connection it can use.

Another possible solution is to download the macOS installer app to your MacBook (in the App Store), then use DiskMaker X to make a bootable installer disk (you need an erasable USB flash drive at least 8GB), then boot the Mini from that. This might need a network connection, but as long as the installer is for the latest version of macOS, it should only need to check for &amp; download the latest firmware for the Mini -- your iPhone hotspot should be able to handle that.