What credit or debit card did you use? If you decide to dispute the try, please contact the bank that issued the card you used.
Apple is not a bank and doesn’t participate in the refund process other than showing you the last 4 digits of the Apple Pay number associated with your payment card.
You’ll want to contact the merchant about the refund. It’s their website that claims 7 to 14 days.
If the merchant claims to have sent the refund, please ask for the Acquirer Reference Number (ARN) that is the number used by Mastercard, Visa etc. to track refunds. That is the number your bank needs to track the refund the merchant claims to have sent. If the merchant won’t provide the number they probably haven’t sent the refund.