Unable to add payment method to my Apple ID

Why can’t I remove or add a new payment

See -> Remove a payment method from your Apple ID

Remove a payment method from your Apple ID - Apple Support

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If you can't remove a payment method

If you have subscriptions like iCloud+, have an unpaid balance, or you use purchase sharing, you must keep at least one payment method on file.

• Do you have a subscription? You can cancel iCloud+ and cancel other subscriptions from Apple. When your subscription period is over, remove your payment method.
• If you're in a Family Sharing group and you use purchase sharing, the family organizer must have a payment method on file. If you're the family organizer, turn off purchase sharing, then remove the payment method.
• If you have an unpaid balance, you might not be able to remove a payment method. Instead, change your payment method.
• If you still can't remove a payment method, contact Apple Support.

You cannot remove a payment method until you have added a new one.

To add and delete a payment method, go to:

Settings → Apple ID → Media & Purchases → View Account → Manage Payment

Select Add Payment Method. Once your new payment method has been added, you can delete the old one.

You can find more useful information here:

Add a payment method to your Apple ID - Apple Support