Solved: add child account verify Done button grayed out credit card location
I'm leaving this here for other confused parents. I tried to add a child account many, many times. Each time I entered a credit card in the adult verify screen, the "Done" button was grayed out. I tried my Apple subscription payment method, my phone's Apple Pay method, one in the Wallet, etc. This screen does not want just any payment method.
The Verify screen will NOT proceed unless you have a valid payment method, name, and address in the Settings->[Your Apple ID]->Payment and Shipping option. If you don't yet, add a payment method, name, and address there first BEFORE adding the child account. That card is what the Add Child process verifies against.
You will know you've got it right when the Add Child Verify screen asks just for that particular card's CVC number, not an entire card number.
Note: mods, please leave this post here, because a child who finds this post will still have to log in to the device, then the Payment and Shipping screen with the user's Apple ID, then have a valid payment method to make their own account.