you can not ship or run the snap command itself in a snap (even if you’d ship it, it would not be able to talk to the snapd server outside of your snap) …
snaps do have a builtin snapctl command you can use, this allows a few of the known snap commands to enable snaps to gather info about themselves … among them is snapctl services that lists shipped services and their status:
$ snap run --shell htpdate-daemon.htpdate
$ snapctl services
Service Startup Current Notes
htpdate-daemon.daemon enabled inactive -
$ exit
$
you will not be able to get any info about other processes outside of your snap (like modemmanager) though …
… that said … if you own a brand store it is possible to grant access to the snapd-control interface and query the snapd API (see the “apps” paragraph):
for lsusb you can just add usbutils as a stage package and add some extra interface plugs (hardware-observe, raw-usb i think)