Harnessing high-dimensional entangled states of light presents a frontier for advancing quantum information technologies, from fundamental tests of quantum mechanics to enhanced computation and communication protocols. In this context, the spatial degree of freedom stands out as particularly suited for on-chip integration. But while traditional demonstrations produce and manipulate path-entangled states sequentially with discrete optical elements, continuously-coupled nonlinear waveguide systems offer a promising alternative where photons can be generated and interfere along the entire propagation length, unveiling novel capabilities within a reduced footprint. Here we exploit this concept to implement a compact and reconfigurable source of spatially entangled photon pairs based on parametric down-conversion in AlGaAs nonlinear waveguides arrays. We use a double-pump configuration to engineer the output quantum state and implement various types of spatial correlations, exploiting a quantum interference effect between the biphoton state generated in each pumped waveguide. This demonstration, at room temperature and telecom wavelength, illustrates the potential of continuously-coupled systems as a promising alternative to discrete multi-component quantum circuits for leveraging the high-dimensional spatial degree of freedom of photons.