to their tunable coupling to dissipative environments. Here we realize programmable local reservoirs for superconducting qubits through parametrically driven coupling to readout resonators, creating energy-selective incoherent pump and loss. Using coupled superconducting qubits, we autonomously stabilize entangled single-excitation states with fidelity up to 90.8%. We probe the stabilization dynamics under varying initial conditions and bath parameters, and implement robust classical shadow estimation for accurate and scalable state characterization. Finally, we numerically study a configuration where the engineered pump and loss share a common dissipative mode, leading to reservoir-mediated interference and classically correlated steady states. Our results demonstrate a scalable and hardware-efficient framework for dissipative preparation and control of correlated many-body states in superconducting circuits.