Hi,
Try to refresh the Outlook permission because sometimes the app get stuck with an old authentication token even if the Authenticator is already updated.
Do this. Open the Outlook app, tap your profile icon on the top left. Go to the settings gear, choose your email account. Scroll down and tap Reset Account, not delete. This only refresh the sync tokens. Close Outlook and open it again.
This usually forces a new MFA check and the email start syncing again. Hope this help. Let me know if you need more assistance.
I hope this helps!