Using Outlook for iOS for personal email and calendar management
Authentication app is device/installation instance specific.
So, if you change device, or reinstall the app, the code is not automatically sent to the the app on the new device or the reinstalled app. It will be still sent to the app on the old device/old install.
If you’re on the sign-in page and can’t access your "old" authentication app, click “I can’t use my app right now.” Then look for an option like “Show more verification methods” to see if you have a backup (e.g., a phone number or alternate email).
If you don’t have access to any of the options listed, select “I don’t have any of these.” This will begin the recovery process. As part of that process, Microsoft will let you add new contact information — but only after a 30-day waiting period.
This 30-day delay is intentional. It’s a security safeguard designed to protect users in case someone else tries to hijack their account by changing recovery info. The wait gives the rightful owner time to notice and stop unauthorized changes.
Unfortunately, this policy cannot be bypassed. Microsoft explains it further here.