Core was originally bankrolled by the Sirian houses as a means of exerting edge worlds influence, which gave them a compelling reason for all their equipment. That still exists to some degree (I mean, it's not as if they have enough of an economic base to even compare with the Order, so there has to be more going on there), although the "state" language throws that off. But yet again, the Core always was internally ambitious.
I think the Core nowadays does a reasonable job of remembering that the Core's strength is dependent upon providing services to those who fund them. Despite things like APM and Iridum export, that is definitely not enough to allow the Core to field entire battlegroups in an area that chews supply lines up and spits them out. If it was just the resources of the Core and the resources of the Order, the Order would almost certainly win, but the Core don't have to be self-sufficient and never really were in the first place. The Order are + shadow support from other organisations.
THE SYNDIC LEAGUES
(A co-operative of Rheinland's outlawed trade unions, determined to take the underworld for themselves.)