Spotify only allows their gift cards to be redeemed for a Premium Individual plan. Gift cards can not be used with Duo, Family, or Student Memberships. For more information please see section 4 of their terms and conditions here https://www.spotify.com/us/legal/gift-card/.
4. Card Redeemable Only for Premium Subscriptions; Cannot Be Used in Conjunction With Any Discounts
The Card is redeemable only for full price standalone Premium subscription months. Gift Cards, eGift Cards and other currency-denominated Cards cannot be redeemed for discounted or group subscriptions (such as student discounts, trial offers, Premium for families, or offers combining Premium with other companies' products or services).