How do I show a component's details in the actor details?

Not that I am aware of. The only way for pure blueprint projects to work with c++ is to make a custom plugin and pack it, then add it to a blueprint project.

You can just use a ACameraActor as the class

UPROPERTY(BlueprintReadWrite, EditAnywhere)
TObjectPtr<ACameraActor> Camera;

The cinematic camera is derived from the camera actor class so it will work with the uproperty.