This only happens in Android.

Some cookies that are set during an authentication workflow in the inApp browsers are not shared back with the app WebView.

This does not happen with the Moodle Session cookie or other cookies such as Matomo ones.

As a side effect, if we are embedding something from the same external site where the authentication happen, the external site will ask the user to re-authenticate (in Android, in iOS it will work as expected are the cookies are there)