Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
I tested this behavior in my own test tenant with Software OATH tokens enabled and was unable to reproduce the issue.
I tested with a newly created account and, after selecting "Set up a different authentication app", the registration flow proceeded normally and displayed the QR code for a third-party authenticator app. I was then able to complete the registration successfully using the generated verification code.
I also tested through My Sign-Ins > Add sign-in method > Microsoft Authenticator > Set up a different authentication app, and the option worked as expected in my environment.
In the meantime, please check whether any Conditional Access policies are applied specifically to the affected account and differ from the users who are able to use Keeper successfully.
If the affected account is configured the same way as the other users' accounts and the issue persists, I recommend submitting a support request through the Microsoft 365 Admin Center so Microsoft Support can investigate further.
For instructions, please refer to: Get support - Microsoft 365 admin | Microsoft Learn.