The snap version of OBS-studio doesn’t support virtual camera. It seems that snap apps can’t install v4l2loopback.ko kernel module and access to /dev/video0.
access to /dev/video0 is provided by the camera interface, make sure to have it connected …
… and yes, indeed, snaps can not just run modprobe (for security reasons) … while there is a module-control interface, this is normally only granted in IoT context for snaps coming from a dedicated brand store …
so i fear you will need to set up your loopback device by hand on a system level … (note that v4l2loopback works fine with snaps beyond this limitation)