Simply having a boot volume group with a System snapshot in it won’t get your Mac to start up from that disk, particularly if it’s an Apple silicon model. Some details.
bless
This has changed greatly over the last few versions of macOS, and differs between different types of Mac. Here’s an outline.
One command, bless, used to do it all, copying boot.efi to the right place and declaring the volume bootable in its header. Where are we with Big Sur and M1 Macs?
You want to boot your Mac from an external drive, but it doesn’t work. A diagram to explain what can go wrong, and how to fix it.
The command bless used to be able to control all things to do with booting, but has become steadily less useful with the advent of SIP and others.
The Eclectic Light Company 