Apple Account Verification Prompt
After changing your email password and waiting for about 24 hours, your phone will detect a password change and initiate a Apple Account Verification to sign you back in. Your phone will prompt you with an "Apple Account Verification" message. You will have the option of "Not Now"/"Cancel" or to open "Settings".
Handling Popups
If you cancel out of these popups, you will eventually get a prompt to sign in with your WSFCS email address already populated and a password field. Do not enter your email password here, as this will attempt to sign you in through Apple's servers, and your account is authenticated against Microsoft.
You will receive a verification failed message if you try.
Update Apple Account Settings
Cancel out of the popup and open the "Settings" app. Under your name at the top, you should see a box that says "Update Apple Account Settings".
Open that, and you will see a prompt saying "Some services require you to sign in again."
Click "Continue".
Apple Account for Your Organization
You will be prompted with an "Apple Account for your organization" window. Continue through that prompt to complete the sign-in process. You will see a Microsoft login window and be asked for your email password.
You can check the box that says "Don't show this again" and say "Yes" to stay signed in when prompted, however this will not prevent you from having to sign in again when your password changes the next time.
By following these steps, you should be able to successfully sign back into your managed Apple ID using your Microsoft credentials. If you have any questions or need further assistance, feel free to ask!