Am not the OP but I’m pretty familiar with standard US account setups for education. Basically, the computer has profiles set up so that a student is accessing “their” files via the intranet. The local computer in front of them has %APPDATA% and whatnot, but that stuff gets wiped to make sure that students can’t jack stuff up. But students (and teachers, for that matter) usually have access to their own “Documents” folder via the intranet.
Think less “their stuff gets wiped every time they log out?!?!” and more “students often don’t use the same computer every time they use a computer.”
The thing is, I think your IT Department is probably wrong about how big a problem the %APPDATA% thing is (based on my experience with school district IT departments, this should not be shocking). OBSIDIAN installs into the %APPDATA% stuff, but the student notes would not actually get wiped — because the vault would just be markdown files on their intranet folder.
It’s basically the same thing as how you can absolutely get a school IT department to install Minecraft — but the session data and all won’t be saved, sure. But if the student saves their maps to their intranet folder, it’s fine.
As for Obsidian, there’s nothing stopping IT from adding it to the %APPDATA% image as a “default installed program” — tho they probably won’t do it for you until over the summer.