apple gift card balance not in my apple tv app

Gift Card balance would be transferred to your Apple ID account, applicable to any of your devices where you are signed in with that same Apple ID account.

For devices that allow for multiple accounts, such as modern Apple TV boxes, verify that the intended account is the active account.

How to redeem your Apple Gift Card or App Store & iTunes gift card - Apple Support

Check your Apple Account balance - Apple Support

Add money to your Apple Account balance - Apple Support