how to add my redeemed gift card as payment source for iCloud storage
I see where I can change source of payment for iCloud and app storages, but don't see how to make it use my redeemed gift card balance instead of my credit card.
It will be taken from any redeemed store credit you have then from a credit card.
How iTunes Store purchases are billed - https://support.apple.com/HT201359 - When you make a purchase, content credits are used first, followed by Gift Certificate, iTunes Card, or Allowance Account credits. Your credit card or PayPal account is then charged for any remaining balance." You can't change the payment type order.