How I remove the “add payment” in the App Store

Read again -> Related Article: Remove a payment method from your Apple ID

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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 usually need a payment method -

You usually need to have added a valid payment method to your account. Even to re-download or update apps and for free apps. You can find the acceptable payment methods for your country here;

Payment methods that you can use with your Apple ID - Apple Support

M1 Mac mini, macOS 13.4;  Watch, series 7 GPS/cellular, watchOS 9.5; iPad Pro 2nd Gen, iPadOS 16.5; iPhone 12 Pro, iOS 16.5; TV 4th Gen, tvOS 16.5; HomePods, audioOS 16.5 and Airport Express w/ Airplay 2