Hi,
Thank you for sharing your question. I understand how frustrating it is to set up Outlook on a new phone when Microsoft Authenticator is inactive and keeps looping during sign‑in. It’s stressful when both apps depend on each other, and you can’t regain access to your account. When Authenticator is unavailable, the system may repeatedly request verification because your old phone was the only registered authentication method. To resolve this, you will need to use an alternate recovery option such as your backup email, your phone number, or the recovery codes you may have saved earlier, and from there you can reset your sign‑in methods at https://aka.ms/mysecurityinfo. If no alternate method is available, the system may require account recovery through the Microsoft account recovery form to regain access and re‑register Authenticator on your new device.
I hope this helps.
Best Regards,
Noel