When you go to install macOS, you should be presented with a notice to assign an Owner to the new installation. Did this occur? It occurs at the very beginning of the install process before any installation files are transferred.
Yes, got this, authenticated against the admin.
Also, make sure you erased the whole physical external drive instead of just erasing an existing volume. Many external drives come setup with odd partition layouts, file systems, and may even contain hidden items which can sometimes affect how an OS may work with it. Unfortunately Disk Utility now hides the physical drives from view by default. See the following Apple article for erasing the whole physical drive:
Yes, properly erased disk from Sequoia Disk Utility.
What is the make & model of this external SSD? Not all external drives are compatible for booting macOS.
Two different setups. One Apple branded flash in a OWC enclosure. One Newertech drive dock with 2TB Hitachi drive.
I would also try using another USB-C cable, making sure it is a high quality cable.
I have tried a couple known good working cables.
Is this external drive connected directly to the laptop? If not, then try connecting it directly.
Directly.
You can also try connecting the external drive using a powered USB3 hub to see if that makes any difference. I have seen some users report they can only access their external data drives through a hub instead of directly attached to an M-series Mac.
FYI, that external macOS boot drive will only work to boot that one M-series Mac where the macOS installation occurred.
I hate that, but I can live with it. As a Pro Mac tech for the last 40 years, this inability is a major hindrance. I can still do a clean install when the time comes and migration assistant to move the data.
Disconnect all other external devices in case one of them is causing a problem.
Done
Why not just boot to the internal SSD and save all the data to the external SSD?
Internal is too small to accommodate User data, and moving complicates installation and maintenance.