Are headless stores compatible with auto-fulfilled Gift Cards? (not on Plus plan)

[christian_s_dev]

We have our store configured to auto-fulfill gift cards in the settings, but when we tested purchasing a gift card, no e-mail was received, and I see on the order page that we have to click "Send Gift Card." We are a headless store, are headless stores compatible with auto-fulfilled gift cards?

The order was created using Headless Storefront APIs.