No option to add a gift card in apple wallet
It says that you can add random gift cards to your apple wallet but there is no option that actually says “add gift card”
The gift card has to support being added to the Wallet. If this is an Apple gift card, those get redeemed before they're used, so they're not eligible to be added to Wallet nor do they need to be. See:
How to redeem your Apple Gift Card or App Store & iTunes gift card - Apple Support
For other cards, check with the issuer to see if they support Wallet. If so they should provide instructions.
Regards.