It is now possible to share keychain data from App Clip with the full app:
Starting with iOS 15.4, information that the App Clip stores in the keychain is accessible to its corresponding full app. To make sure only the corresponding full app receives access to keychain items stored by the App Clip, the system uses the com.apple.developer.associated-appclip-app-identifiers and Parent Application Identifiers Entitlement entitlements. When you create an App Clip with Xcode, it adds the Parent Application Identifiers Entitlement. It automatically adds the com.apple.developer.associated-appclip-app-identifiers entitlement when you archive the app that contains the App Clip.
https://developer.apple.com/documentation/app_clips/sharing_data_between_your_app_clip_and_your_full_app