Posit people look at this posts from time to time, and you could also try to contact technical support from within Posit Cloud itself but I suspect there is a non-trivial technical reason or ven maybe a licensing issue that prevents them to make a binary available.
Even if you manage to get rstan installed in a base project you can share with your students, I doubt they will be able to do much with it considering the 1 GB RAM limit for free accounts.