So we have two scenarios
1: Franz take it over at some point after the Heart of Darkness have been published. He run it in benign neglect for a decade and half until it‘s lost in WWI. likely the local Austrian garrison keep fighting the until the end of the war. The size allow them to do so. afterward It likely end up under French control with some areas given to Portugal.
2: Franz gain it earlier at alt-Berlin, this will have bigger effect, we will likely see a expansion of Triest and Fiume, money made in Congo could go to expand these ports, as they grow in importance, this also demand a expansion of their infrastructure, and the infrastructure conneating them with the rest of Austria, we likely see expansion of the railroads to them or even the Triest-Vienna canal being dug. The navy likely grow in importance. In WWI this means that Austria can far easier send soldiers to Italy and the Austrian navy will be a problem. Of course that ignore the foreign policy effect of Austria being more active in Albania, we could very well see Austria messing more in the Balkans. Of course in al this case the Congo Free State won’t get the same benign neglect, but at the same time Franz is unlikely to be cartoonish evil as Leopold ended up being.