you need to ship the vc4 libs yourself from its own part in snapcraft.yaml, then using the opengl interface in your app should allow access to the devices that the rpi bootloader firmware for de/encoding offers …
ah, you did not talk about two snaps in your initial post … it might indeed be that the dotnet runtime needs the libs and interface connection available as well (my dotnet experience is close to zero).
is there a particular reason that you keep them separated ?
you could use dotnet as a stage-snap so everything is executed in the same environment.