Here's what you can do to resolve this:
Choose the Account for Passwordless Authentication: If you want to use passwordless authentication with your work account, you may need to disable it for your personal account first. You can do this by going into the settings of the Authenticator app, selecting your personal account, and disabling the passwordless sign-in option.
Use Another Device: If you have another device, you could set up passwordless sign-in on that device for the other account. This way, you could use passwordless sign-in for both accounts, but each on a different device.
Use a Different Authentication Method for One Account: If you want to use both accounts on the same device and only have one device, you might consider using a different authentication method for one of the accounts. For example, you could use passwordless sign-in for your work account and a different method, such as text messages or email verification, for your personal account.