However, did not find any way to access this variable in the Data Provider Class. Do you have any tipp?
The session_id is actually a static attribute specified in the IF_HTTP_SERVER interface. Because of the way in which ABAP sessions work, it is not possible to have two HTTP requests processed simultaneously in the same ABAP session, so I guess it makes sense to have the session_id as static.
Anyway, you can do something like this in your DPC_EXT class to obtain the session:
DATA(lv_session) = cl_http_server=>if_http_server~session_id.