Why can I not add a card even though I have the iPhone 13, have storage, and am signed into my Apple ID?

If you can't make purchases or update apps, including free apps, you need to update your payment method or add a new one. If you already verified that a payment method is available in your country or region and you're still having trouble, learn more.

Based on your country of residence and country you have selected under your Apple ID --> Payment methods that you can use with your Apple ID - Apple ...

Have you a Debit/Credit card that is issued to you that is valid internationally and is from the same Country / Region as your Apple ID.

Know it here --> If your payment method is declined in the App Store or iTunes ...

Check the following

1. The payment method that you are adding is of the same country as that of App Store Country on your iPhone
2. You have a valid payment plan debit/credit card from an authorised bank from the same country
3. Payment methods that you can use with your Apple ID - Apple Support
4. Learn more about family purchases and payments.
5. Please check if your Debit/Credit card is valid internationally

If you can't choose None as a payment method only if...

1. If you have an unpaid balance or payment due
2. If you have a subscription that automatically renews
3. If you're using the iTunes Store or App Store for the first time
4. If you are not in the country or region you’re creating an Apple ID for
5. If you changed your country or region
6. If you're a part of Family Sharing