“Sent” means Shopify handed the campaign off for delivery; it doesn't guarantee every subscriber got it in their inbox or even entered the final send audience.
Check the specific form’s table in Site settings > Forms and the Dashboard spam inbox; if both are empty despite successful live tests and notifications, it needs Webflow Support to investigate account-side records.
Shopify local delivery appears only when the cart, fulfillment location, verified address, delivery zone, and checkout path all meet its eligibility rules.