MacBook Pro unrecoverable error during system restoration
The rhetorical question is why did the Apple Store staff not realize this problem before sending us home to figure it out ourselves, when they had advised us to restore our user content from a backup?
The failing keyboard and touch bar on our MacBook Pro (purchased 12/2018) was replaced under warranty, wiping out our previous disk contents and OS (Monterey). When we picked it up, it had an older OS (High Sierra). When we tried to restore our user content from a Time Machine backup using the Apple Migration Assistant, it said the backup OS was newer than the machine OS and needed to be upgraded. I tried using the Time Machine backup to restore our previous OS (Monterey) and user content - and that's when the "Unrecoverable error, SecurityAgent was unable to create requested mechanism builtin:prelogin." showed up at the end of the lengthy restoration process.
Then I tried the "Turn on your Mac and immediately press and hold Command (⌘)-R" approach to reinstall a later version OS (it picked Catalina). Same unrecoverable error showed up at the end of the lengthy reinstall.
Finally, I tried "Option-Command-R during startup", got the Internet Recovery spinning globe screen, and was offered a menu that included "Reinstall macOS Ventura". This lengthy installation completed without the unrecoverable error. And finally the Apple Migration Assistant was happy to restore our user content.
It seems the OS backward compatibility issue for the Migration Assistant would be well known to Apple store staff, and they should not have sent us home with a repaired laptop that would not accept a recent backup.