There is nothing additional we can provide if the refund was not approved. You do need to figure out how someone was able to purchase the app on your account.
- If you are the Organizer of a Family Plan with Purchase Sharing, members are authorized to make purchases on your card.
- If someone knows your Passcode, that gives them authorization to make purchases.
- If your Apple Account has been compromised, you need to immediately change your password.
- Review your Purchase History to see what date the app was purchased and it may help narrow down if someone else had your device on that day. View your purchase history for the App Store and other Apple media services - Apple Support
The normal process to request a refund is available here and you don't need to contact the Support Center. You usually get one appeal if it has been denied, then you would get a final decision if it was not approved. In most cases, all purchases in the App Store are final, but at times Apple may issue a compassionate refund. It should never be expected though:
Request a refund for apps or content that you bought from Apple - Apple Support
Once you determine how the charge occurred, we can offer additional steps to prevent that from happening again. The purchase on your device requires double clicking the side button with the amount showing on the screen, followed by verification with FaceID or Passcode, so it is not something that can be done by accident.
You don't get Notifications of purchases, but will receive an email to your Apple ID email address if that is set on your account. The email does not come immediately on purchase and you may see it 2-3 days later. It is not meant to notify you of a purchase, it is only the receipt.