Multi-Factor Authentication settings are not backed up by default as it is required to configure the Tenant Admin Credentials to backup these settings.
In addition, if On Demand Recovery is not configured to backup the MFA settings, it will not be possible to restore those settings, nor can the Phone or Email values found under the 'Authentication contact info' section of the user profile be restored.
Once configured, On Demand Recovery will backup the following MFA settings:
To configure On Demand Recovery to backup the MFA settings:
NOTE: The account you specify either has to have MFA disabled or you have to add the On Demand Recovery IP Address to the list of Trusted IPs for your Azure tenant. Please contact Support to obtain the IP Address if needed.
The following Microsoft article discusses how to configure the bypass for MFA using Trusted IPs: