The behavior of charged vesicle suspensions, commonly encountered in biological and industrial contexts, is largely governed by screened electrostatic repulsions. However, the addition of depletants such as polymers can induce attractive interactions and lead to gel formation. Here, we investigate the rheology and yielding behavior of such a vesicle gel, relevant to a class of consumer products. The combination of experiments and Brownian dynamics simulations enables us to establish connections between macroscopic rheology and microstructural features. Oscillatory tests reveal a predominantly elastic response at small deformations, followed by yielding upon increasing the strain amplitude. With increasing shear rate, the flow curves feature a yield stress regime, followed by shear thinning and, eventually, a Newtonian-like response (viscosity plateau). We find that, in both oscillatory and shear-rate-controlled tests, the yielding transition is accompanied by nonmonotonic trends in structural heterogeneity. Fitting the flow curves with the recently introduced three-component model reveals that structural heterogeneity peaks near the crossover from the yield stress plateau to shear thinning, while homogeneity is recovered in the Newtonian-like regime. Numerical creep tests exhibit rich phenomenology, including Andrade-like deformation, delayed yielding, and resolidification, whose persistence even above the dynamic yield stress highlights the ductile nature of gels with competing attractive and repulsive interactions. Overall, our study highlights distinctive rheological and structural features of gels with competing attractive and repulsive interactions, providing insight into how microscopic heterogeneity controls yielding and flow.