the reboot interface doesn’t seem to exist however, +1 from me for auto-connect to shutdown. It is reasonable and expected functionality for the snap.
I saw that other snaps from your account have been granted shutdown in the past, however, shutdown is now a super-privileged interface. In this case, you should apply for account verification as well.
I also thought that since the software is not for general public use that a brand/dedicated store may be worth looking into to add more control for where the software can be installed.