WSO2 API Manager 4 - How to add claims in X-JWT-Assertion token when scope is a Shared Scope and not 'openid'

I am using some Shared Scopes to restrict access to ressources of my published APIs.

Now I am trying to add user information in the header X-JWT-Assertion for the backend : user email for instance. So a claim that is already existing in the standard claims dialect.

I found that post as an example of what I am trying to do, but it is only working with scope 'opendid'.

https://jabhax.medium.com/add-claims-to-jwt-for-wso2-apim-using-inbuilt-gateway-jwtgenerator-393b0bf873b3

I tried to add my Shared Scopes as new OIDC scope in Carbon console, but an error message is saying that it is already existing even if it is not displayed in the GUI (I guess Shared Scopes and OIDC scopes are stored in the same table in DB)

How can I add user information inside X-JWT-Assertion headerreceived by the backend when scope is not "openid" but my own Shared Scope ?