How to make a bootable, *usable* macOS USB key (NOT an installer)? 2011 iMac running Sierra
I would like to have a copy of macOS that I can actually boot from and use on a USB key, so that I can run Carbon Copy Cloner from it to make backups of any volume on the machine at any time.  I previously had a dedicated small partition on one of my drives for this purpose, but that drive died and going forward I would rather have this on a USB stick.
To be clear, I don't want a &quot;bootable installer&quot;.  I want a fully functional bootable macOS on the stick, i.e. it boots into Finder, etc.  All the answers I've found related to this, are about creating bootable installers.
Can this be done and if so, how?
Carbon Copy Cloner or SuperDuper! can to clone to an external USB drive and it be bootable. (At the present moment they do not work on macOS Big Sur to make bootable clones.)
For versions of macOS prior to macOS Mojave, other options include:

Booting with a macOS USB Installer and then use Disk Utility to image the drive to another USB flash drive.

Creating a macOS USB Installer on one USB flash drive and actually installing macOS to another USB flash drive.

 (This option actually can be used on macOS Mojave and later.)