Start with the right checks.
Restoring Authenticator is not the same as restoring every account’s sign in credentials. Work and school accounts can require registration again.
What to do next.
Inventory the accounts shown in the old app without copying secret codes into a document.
Follow Microsoft’s backup and restore instructions for the applicable phone platform.
Sign in and register accounts that require it, using the organization’s process for work access.
Test the new phone with a routine sign in while the old phone remains available.
Check the result.
Check each important account independently. Seeing an account name in the new app does not prove that approval or passwordless access works.
Stop and get help if…
The old phone is lost, no alternative method works or an administrator must approve registration. Get help with recovery rather than deleting the remaining account entries.