This is not available to EU users yet, even to manually add the info. According to Macrumors, this feature is currently in the iOS 15.4 beta.
When iOS 15.4 is released, users will be able to add a EU Digital COVID Certificate to the Health and Wallet apps by opening the Camera app, scanning the certificate's QR code, tapping on the yellow Health app notification that appears, and tapping the "Add to Wallet & Health" button. Vaccine cards in the Wallet app display a person's name, the type of vaccine they received, the date that each dose was administered, the issuer, and a digitally signed QR code. More detailed immunization records are accessible through the Health app.