Microsoft 365 features that help users manage their subscriptions, account settings, and billing information.
Based on the information you provided, I understand that you recently changed to a new iPhone and can no longer access your email account. The authentication app on the new phone is not displaying the verification code or approval request you need, and you cannot find another sign-in method. You have also tried signing in from both your laptop and phone, but the issue remains.
Since 2FA security policies for institutional accounts are managed centrally, you will need to contact your work's IT administrator or help desk. They will be able to reset your 2FA settings from the backend so you can register your new device without any issues.
You can suggest that they check this article for steps on resetting MFA: Manage user authentication methods for Microsoft Entra multifactor authentication
However, please refer the following article to find your IT Admin: Find the administrator for your work or school account
If you are a sole admin, please follow this link to create a trial tenant: https://www.microsoft.com/en-us/microsoft-365/business/microsoft-365-business-basic?msockid=3eb6980b5c6860e63a588d0c5d1761d6 - after that you will be able to access to Microsoft 365 Admin Center to raise the ticket
Assuming that you have already created an account after registering a free trial and you can go to Microsoft 365 admin center and click "Help & support" icon to raise your ticket. The agent will be able to create a ticket for you under the affected tenant and then transfer this ticket to Data Protection team who could help you to regain access.
Please mention that you are raising ticket on behalf of the affected tenant that you do not have access to. The support team will help you to create ticket on the affected tenant then later on the Microsoft Data Protection team will assist you.
Note: This process will take more time than usual (7-14 working days) for your account to get access again as Data Protection is always overwhelmed with the number of tickets. As I am user, I do not have access to Microsoft internal system to assist or push this process to be quicker.
On the other hand, if you do create the trial and it resolves the issue, please remember to cancel the subscription afterward to avoid any related charges. Thank you.