The fields of autonomous systems and robotics are receiving considerable attention in civil applications such as construction, logistics, and firefighting. Nevertheless, the widespread adoption of these technologies is hindered by the necessity for robust processing units to run AI models. Edge-AI solutions offer considerable promise, enabling low-power, cost-effective robotics that can automate civil services, improve safety, and enhance sustainability. This paper presents a novel Edge-AI-enabled drone-based surveillance system for autonomous multi-robot operations at construction sites. Our system integrates a lightweight MCU-based object detection model within a custom-built UAV platform and a 5G-enabled multi-agent coordination infrastructure. We specifically target the real-time obstacle detection and dynamic path planning problem in construction environments, providing a comprehensive dataset specifically created for MCU-based edge applications. Field experiments demonstrate practical viability and identify optimal operational parameters, highlighting our approach's scalability and computational efficiency advantages compared to existing UAV solutions. The present and future roles of autonomous vehicles on construction sites are also discussed, as well as the effectiveness of edge-AI solutions. We share our dataset publicly at github.com/egirgin/storaige-b950