When I restart in Recovery mode and attempt to enter Startup Security Utility, I'm asked for my MacOs Password but not given a dialogue in which to enter it. So I'm completely unable to advance (I wish to enable booting from external SSD

Reinstalling macOS over top of itself should not affect your data, but you should definitely make sure to have a good backup first just in case.

Do you have multiple admin user accounts on this Mac? If so, then try authenticating as one of the other admin user accounts. I have seen some bugs with the Intel T2 Macs where I was unable to authenticate with any admin user accounts even though I could log into each admin user account when booting normally (including unlocking the Filevault using each user account even when rebooting each time in between attempts). I decided to try deleting one of the admin user accounts which then allowed me to authentic in Recovery Mode, but I could only authenticate to the newly deleted (fully deleted) user account as that was the only one on the list provided. Even though I was able to access the Startup Security Utility, I decided to "Restore" the firmware of that T2 Mac just to be safe since obviously something was wrong with the laptop and I didn't have time to deal with any other possible issues or side effects. Some of the new changes to both macOS and the Apple hardware do contain bugs and design oversights and unfortunately there are several ways this new system can break down requiring a reinstall of some sort.

You can attempt to "Revive" the firmware on the laptop, but I don't think the "Revive" option will fix your issue. Reinstalling macOS over top of itself is probably the best option to "fix" your problem.

If you end up performing a clean install by first erasing the Container instead of just reinstalling macOS over top of itself (the former option destroys the data on the drive, while the latter option should not affect your data or apps), then I would instead recommend "Restoring" the firmware of the laptop as that should also reset the security enclave.

Revive or restore a Mac with Apple silicon using Apple Configurator 2 - Apple Support

You should always have frequent and regular backups of your computer and all external media which contains important & unique data. There are a lot of ways to permanently lose data with an SSD if you don't have a backup.

There are reliable reports appearing on the ASC Forums regarding failed installation of Monterey on older Qualifying Apple Computers. In most cases this is related to having a NON Apple Original internal drive ?  

In the above case - the external Drive is the destination for Monterey Installation. This maybe achieved Only Once the Intended Computer has had Monterey Installed and the EFI Boot ROM has been applied.

The EFI Boot ROM included in Monterey is verifying for Original Apple Drive and if not found , may Balk or fail to upgrade to Monterey. 

Reports indicate the EFI BOOT ROM is Required to Flash the Computer and is a  requirement for a Successful Monterey Installation.

Second part of you original question >>

Use macOS Recovery on a Mac with Apple silicon

from above

• Startup Security Utility: Set the security policies for your Mac. In the Recovery app, choose Utilities > Startup Security Utility. To return to the Recovery app, choose Startup Disk > Quit Startup Disk. See Change the security policy.

While you may not be able to easily change the startup security with Catalina, you still should be able to change the Startup Security setting using Big Sur using Recovery (running Startup Security from a bootable installer also used to work but the last time I tried this I got a message telling me to use Recovery).

Should you ever want to change Startup Security in Catalina to a less restrictive security option, you may have to reset the machine and reinstall macOS from scratch.