Can't change startup disk

Old issue (one month). I've run into problems installing Monterey, period. It seems to take more than one try to get it right. I do an install by the book, then I try booting from that install, and I can't because apparently it was "INCOMPLETE" (what's up with that?), so I go through the whole process again. Regarding "Change your startup disk once", yes, see above, I've tried that, and it's a waste of time. Why is it "once"? Is that all I get? I read that the T2 chip can make changing startup disks more of an issue, but I can't find any indication of a T2 chip on this computer. How would I find it? BTW, “Loading startup options” has not appeared at all, in any of the strategies I've tried. I've clicked on the Options preference on a black screen, and been presented with the three potential startup disks, but if I click one other than the current boot drive, I get the "Unable to set startup disk" box. How many times must I re-install Monterey?

I can't say I understand all of the issues at play here, but overall it sounds as if I may not be able to install as many systems on as many individual discs as I had planned, owing to the security system(s) now built into Monterey. O.K., I can live with that. To back up some of the observations in the articles you linked, I did have a hard time installing OS 12.3.1 more than once, and when I did succeed, it wasn't precisely that, it was 12.3 period, rather than 12.3.1 that got installed. The note "BTW, I forgot to mention that I had to boot into Safe Mode in order to install 12.3.1 to the external SSD."...gives me a possible solution to that problem, but there is clearly more to this than there was with previous versions of Mac OS. So I'm reluctant to forge ahead with installing spare systems without talking to Apple Support about this whole issue. Thanks, guys

(one day later) Just for the record, I have by now spent 2 hours on the phone with Apple Support dealing with the security settings on my M1, but I was required to stop before the tech could walk me through setting up a new, spare, bootable drive. I was assuming that, since I had done that many times before, I had the installing-a-new-system part of this process well in hand. I was wrong. After numerous tries, I now have that same 1TB SSD drive, after many installations of Monterey 12.3.1, with an unusable installation on it. The installation stopped and required a restart-which usually indicates completion-but it's still useless. System Applications were installed, no User Library contents, and no users. Only the System and its contents. And that isn't enough to boot from, I have found.

After three long phone calls with knowledgeable support staff at Apple, the problem persists. Even after changing the startup disk security policy (see above), I was unable to install a functional system on a second disc-meaning on a disc that isn't the one the computer booted up with. After many erase-and-reformats and trying to install two slightly different versions of Monterey, this M1 Mini is still unable to establish a useable or bootable system on an external disc. Is it simply forbidden, or physically impossible? I have tried all of the solutions suggested here, and all the solutions suggested by AppleCare experts. All have failed. The only observation I can make is that every install attempt has left behind a stunted version of a system: four folders: Applications(empty), Library (empty), System(not empty), and Users(empty). That's IT. That's all that gets planted on the disc.

OK. Thank you for the information about the T2 chip, and for letting me know that whatever it is that is going on with this Mac is unusual. Next stop: Apple Support. Thanks again.