What do the students need to do?

You've basically just asked "is an XL tshirt big enough for me" without telling us how big you are.

Sounds like you want a video card that supports SR-IOV. Any gpu that supports this is going to be pretty pricey. I think the intel flex 140 or 170 are specifically designed for a scenario you describe but are $2 - $7k and are one of the few that don't require any licensing fees. Which can also be significant. There are more powerful options but the price goes up from there.

For that price though you may be better off just buying 30 used mini pcs? Not sure what the budget or design constrains are though.

Hope that helps or at least gets you in the right direction.

bro, did you know that X11 is network transparent for exactly that scenario. the Xclients (running on a central server) can connect to a remote Xserver on the thin client. Xpra can deal with unstable connections. XDMCP can handle multi user environments. It was like magic back in the day. You could have a GUI app running on your workstation in the office displayed in your living room.

AFAIK they have something like that in wayland, too. not sure how complete it is. didn't try it yet.