How to make a bootable, *usable* macOS USB key (NOT an installer)?
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.)