It sounds like a totally different scenario, and not really related to authentication. As far as I know user context is not available at all. Especially not in PBI Embedded, where the user is not impersonated, but a sinble application token is used. In the "conventional" version the logged in user can be used for row level security, when the datasource is an SSAS cube. But that's not applicabple here.
Folks, correct me if I'm wrong. But I thin you need a different approach here. Authentication tricks won't help you in this regard.