Hybrid moiré excitons form a dense array of electrically tunable single-photon emitters, entailing cooperative optical responses with intriguing consequences. With the strong dipole-dipole interaction, they also realize Bose-Hubbard quantum simulators of emergent correlated matter such as Bose-Einstein condensates (BEC). Here we reveal the characteristic cooperative radiation from condensates of hybrid moiré excitons in twisted MoTe
2 bilayers. In each individual moiré trap, the layer hybridization selection rule dictates that the ground-state exciton is a quantum emitter of orbital-angular-momentum photons, with an exceptionally long radiative lifetime. Ground-state emission becomes pronounced only upon forming condensates, where inter-sublattice dipole attraction and intra-sublattice repulsion together lead to the coexistence of exciton and biexciton BEC with comparable weights. The biexciton (molecular-type) BEC decays through superradiance of path-entangled biphotons, whereas the exciton (atomic-type) BEC is dark at rest and becomes superradiant when it carries a supercurrent. Our findings not only uncover a novel source of entangled light but also establish unique fingerprints for exploring the cold chemistry of atomic-molecular condensates with moiré excitons.