Macbook won't let me boot from external drive because of there's no administrator in the startup security utility

You aren’t seeing the Users directory because of the read-only system volume that was introduced in Catalina: For every system volume named “Foo” there is a second volume named “Foo - Data” that contains your Users directory.

You mentioned that you can boot to Target Disk Mode. If that is still the case, go ahead and do that, but this time on your lifeboat Mac open Disk Utility, go to View -> Show All Devices, and check to see if there is an unmounted (greyed-out) volume next to your target’s “system” volume which has the “- Data” suffix. If so, select it and press the Mount button. You may need to enter a FileVault password at this point.

Alternatively, you can use Terminal on your lifeboat to examine which volumes are available and what their statuses are:

$ diskutil list
$ diskutil apfs list

You can also do the same thing when booted into Recovery mode (Tools -> Terminal).

UPDATE:

With your target in TDM and mounted on your lifeboat, run the following. (Make sure not to disconnect your target or add/remove any other devices from your lifeboat, otherwise the disk numbers may change and your data volume might not be on /dev/disk4s1.)

$ sudo diskutil verifyVolume /dev/disk4s1

UPDATE 2: As I keep seeing more and more reports like this, I suspect that you are also in the camp hit with the unfortunate Big Sur installation bug. I suggest reading through that before continuing to debug.