Rapid urbanisation has intensified the pressure on municipal waste management, exposing the limits of conventional, capacity-driven service models. Edge-computing now enables smart-waste solutions that improve operational efficiency by processing data closer to the point of collection. Yet, as concern grows over the societal impact of technology-enabled urban systems, edge-enabled smart city systems are increasingly expected to demonstrate not only technical efficiency but also sustainability, social, and business value. Evaluation practice, however, remains siloed: low-level system performance is typically assessed separately from the broader public-value outcomes at stake, leaving decision-makers without a coherent basis for judging whether a deployment delivers value beyond the technical layers. This paper addresses that gap by proposing a three-dimensional KPI-KVI framework for evaluating edge-enabled smart waste management systems, in which measurable Key Performance Indicators (KPIs) are explicitly linked to the higher-order Key Value Indicators (KVIs). The framework is derived from a focused review of evaluation literature, stakeholder input, and a live edge-IoT pilot in Valencia, Spain, conducted within the COP-PILOT Horizon Europe project. Twenty KVIs, operationalised through twenty-two KPIs, are organised across sustainability, social, and business-value dimensions and mapped to corresponding value outcomes. Pilot measurements indicate an approximately 53% reduction in memory usage through split services and a 6.9-second actuation time from sensor activation to service deployment, providing evidence at the system layer for the framework’s efficiency and sustainability dimensions. We do not claim end-to-end validation of public-value outcomes; rather, these results indicate that a split-service edge architecture offers a plausible pathway toward operational efficiency, sustainability, and public value, with wider outcomes to be confirmed through longitudinal KPI-to-KVI assessment.