How is MFA implemented?
By Security Defaults: You would need to disable it entirely ( not recommended)
With a Conditional Access Policy? Exclude the mailbox from the policy
per user? Disable the per user option for that mailbox
You would also need to verify that MFA registration is disabled for that mailbox
App passwords do not work with modern auth: https://learn.microsoft.com/en-us/entra/identity/authentication/howto-mfa-app-passwords
Best solution: Leave MFA as is for all users and send email using an OAuth App instead: