If you have accidentally deleted an account from the Microsoft Authenticator app and are unable to add it back, you can follow these steps:
Go to the Microsoft account security page on your computer (https://account.microsoft.com/security/).
Select "Security basics" from the menu.
Under "More security options," select "Authentication methods."
Choose "Microsoft Authenticator" from the list of options.
Follow the prompts to verify your identity and add the Authenticator app as an authentication method for your Microsoft account.
Once you have added the Authenticator app as an authentication method, try adding your account again in the Authenticator app on your mobile device.
When prompted for a code, open the Authenticator app on your mobile device and select "Add account."
Choose the type of account you want to add (e.g., Microsoft account, work or school account, etc.).
Follow the prompts to enter your email address and password.
You may be prompted to verify your identity using a notification or verification code.
Once you have verified your identity, the account should be added to the Authenticator app and you should be able to use it to approve sign-ins again.