See How to share apps and purchases with your family - Apple Support. While purchase sharing is enabled anyone other than the family organizer is unable to edit their payment settings, which would not in any event be used for purchases from the iTunes or App stores. You can add store credit to your Apple ID (see Add money to your Apple Account balance - Apple Support), which is not the same thing as Apple Cash, which can generally be used to pay for things instead of the organizer's payment method, or you can turn off purchase sharing, add your own method of payment, make a purchase, and then turn purchase sharing back on once you are done.
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