A Microsoft file hosting and synchronization service.
I checked my 4 devices and my wife's PC to see what versions of OneDrive were installed:
Two PCs operating correctly and requiring two-factor authentication via the app to open Personal Vault were:
OneDrive version: Build 23.054.0313.0001 (64-bit)
Three PCs only requiring PIN without two-factor authentication were:
OneDrive version: Build 23.061.0319.0003 (64-bit)
Both versions were available on Microsoft site for download. I downloaded the version that was on the working PCs (xx54.0313.001).
On one of the PCs that had the PIN only version (xx61.0319.003), I uninstalled and reinstalled Build 23.054.0313.0001 (64-bit).
After restarting and confirming the intended version was now installed, I found it still was allowing access to the Personal Vault with only the PIN.
This inconsistency is a continuance of the frustration I've been dealing with for a couple of months working with Microsoft....