One thing that may be worth mentioning.
When installing to an external drive, you DO NOT want to use the same USBc port that is used for booting that Mac into DFU mode.
For example, with the m4 Minis, the CENTER USBc port on the back is the "DFU port".
So,
don't use that one.
For other Macs, it varies as to which port is the DFU port.
You have to check online for this. Try here:
Learn how to find the device firmware update port on your Mac.
support.apple.com