How to enable SSO login from ios native app to a webview

I have the same use case.

We have one native application that opens multiple web application using webview on user demand.

The same authentication method is used, in this case, OpenID Connect.

When the user first authenticate against the native application on iOS, it opens up a Safari Webview Controller, the user complete the authentication requirements, where their are redirected back to the native application.

Later on, the user click on a button and open a webview that displays a web application. We want this user to be able to authenticate on this web application. But cookies are not shared between the Webview and the Safari Webview Controller, so session isn’t found and user has to re-complete authentication requirements.

Is there any workaroud to share cookies sessions? Or at least, would the webview be able to open a Safari Webview Controller on authentication requested? So the cookies would be found?

But in this case, how to pass authentication code? Should we register yet another callback on the native side so the native application could pass the authentication code to the webview / web application and the web application could exchange that code to complete authentication?

It’s a bit overkilled, isn’t it?