I don’t think the snap helper is ment to be run in a template. The only thing a template is for is to install software and create the read-only image for the AppVM’s. The package triggers during installation will of course run but any services will need to be started/run in the AppVM. Maybe there is a service that needs to be configured for it in the AppVM?
I have been struggling with getting snaps running just like you. I have found a number of applications that I would like to try for my nonprofit but so far nothing has worked out in my favor. None of my qubes menu entries are successful at launching anything and it appears to me to be file permission and path issues. The snap isolation seems to be what is getting in the way and a service is likely missing needed to bridge the gap to be able to launch anything. I just have not had the time to invest to figure out how this is all supposed to work. I never used snap on any simpler environment so qubes is just an additional complication.