Mac mini m4 cannot start with external ssd

Not sure how you made the bootable drive but when I got my Mini M4 my previous bootable drive would not work. I had to remake the drive. Looks like not compatible with the new architecture of the Mac even though both had the same level of OS (15.1). I always use CCC and install the OS on that drive using recovery mode.

An external bootable drive made on one computer cannot be booted on a different computer especially on the latest versions of macOS and Apple Silicon. There are security measures in place that "key" an external install to a particular computer and owner. This is likely done so that someone cannot take a "generic" bootable drive and plug it into a stolen computer and scape the information from it.

You will need to do a fresh install on the external drive with the exact same macOS version on the M4 and either restore apps and data from a clone or Time Machine backup or from the internal drive.