We investigate the impact of threading dislocations with an edge component (a or a+ c-type) on carrier recombination and diffusion in GaN (0001) layers close to the surface as well as in the bulk. To this end, we utilize cathodoluminescence imaging of the top surface of a GaN (0001) layer with a deeply buried (In, Ga) N quantum well. Varying the acceleration voltage of the primary electrons and comparing the signal from the layer and the quantum well enables us to probe carrier recombination at depths ranging from the close vicinity of the surface to the position of the quantum well. Our experiments are accompanied by fully three-dimensional Monte Carlo simulations of carrier drift, diffusion, and recombination in the presence of the surface, the quantum well, and the dislocation, taking into account the dislocation strain field and the resulting piezoelectric field at the dislocation outcrop. Near the surface, this field establishes an exciton dead zone around the dislocation, the extent of which is not related to the carrier diffusion length. However, reliable values of the carrier diffusion length can be extracted from the dipole-like energy shift observed in hyperspectral cathodoluminescence maps recorded around the dislocation outcrop at low acceleration voltages. For high acceleration voltages, allowing us to probe a depth where carrier recombination is unaffected by surface effects, we observe a much stronger contrast than expected from the piezoelectric field alone. This finding provides unambiguous experimental evidence for the strong nonradiative activity of edge threading dislocations in bulk GaN and hence also in buried heterostructures.