The identity context is opaque to your web service client and web service and you dont need to perform any additional coding or processing in your client or service to support it after you enable identity context propagation.
Which Oracle SOA Suite component directly enables this behavior?
The correct component that directly enables the behavior of identity context propagation without needing additional coding or processing in your client or service after enabling it is Oracle Web Service Manager Policy Manager. Oracle Web Service Manager (OWSM) provides the necessary policy enforcement and security to manage web services seamlessly, which fits the requirement stated in the question.
A. Oracle Web Service Manager Policy Manager
https://docs.oracle.com/middleware/1212/owsm/OWSMC/owsm-intro.htm#OWSMC4166 indicates OWSM provides web service without any additional coding