When dispersed in a nematic liquid crystal, colloidal particles can be driven along the local director by the action of an oscillating electric field. This phenomenon, called liquid-crystal-enabled electro-osmosis results mainly from the unbalanced ionic flows coupled to the distortions of the elastic matrix. Individual particles move ballistically along the local director but feature an anomalous diffusive behavior in the perpendicular direction that we tune by changing the temperature-dependent material properties or the nature of the inclusion. We explore the collective behavior of these phoretic colloids by local photo-patterning the director field. This way, we can force an ensemble of particles to swarm towards a target point, putting into evidence a long-range interparticle repulsion that opposes the centripetal phoretic drive. The resulting two-dimensional clusters feature the coexistence of two non-equilibrium aggregation phases: a growing, inner, solid-like core surrounded by a liquid-like corona of constant width that expands towards the outer boundary. By exploring the dependence of the cluster geometry on the electric field frequency, we put into evidence the interplay of interparticle forces of different physical origin, which are integrated by a simple theoretical model and simulations that reproduce the experimental observations.