Biomolecular condensates are thought to play a pivotal role in cellular organization by regulating biochemical reactants in space and time. Sustained molecular fluxes across condensate boundaries, together with the participation of phase-separating molecules in active chemical reactions such as ATP hydrolysis, call for a nonequilibrium description. Here, we propose a self-consistent framework in which diffusion-drift dynamics and chemical reactions are coupled through a conditional free energy, defined as the excess contribution to the chemical potential. Self-consistency is achieved by deriving this quantity from the same free-energy functional that governs molecular interactions and phase separation. We apply the framework to a minimal client-scaffold system and investigate how active chemical processes and phase separation interact at steady state. In doing so, our approach recovers the fundamental rules previously identified for the emergence of nonequilibrium steady-state fluxes. The model shows that active reactions involving the scaffold molecules can regulate the phase behavior of the condensate. Moreover, nonequilibrium steady-state fluxes are maximal near the boundary between the phase-separated and homogeneous regimes, suggesting that condensates sustaining molecular transport may operate close to their stability threshold. In the same region, client fluxes are also enhanced, revealing an indirect coupling between scaffold activity and client transport. These results provide a baseline for developing more detailed theories of chemically active condensates.