This paper presents field-tested use cases from Search and Rescue (SAR) missions, highlighting the co-design of mobile robots and communication systems to support Edge-Cloud architectures based on 5G Standalone (SA). The main goal is to contribute to the effective cooperation of multiple robots and first responders. Our field experience includes the development of Hybrid Wireless Sensor Networks (H-WSNs) for risk and victim detection, smartphones integrated into the Robot Operating System (ROS) as Edge devices for mission requests and path planning, real-time Simultaneous Localization and Mapping (SLAM) via Multi-Access Edge Computing (MEC), and implementation of Uncrewed Ground Vehicles (UGVs) for victim evacuation in different navigation modes. These experiments, conducted in collaboration with actual first responders, underscore the need for intelligent network resource management, balancing low-latency and high-bandwidth demands. Network slicing is key to ensuring critical emergency services are performed despite challenging communication conditions. The paper identifies architectural needs, lessons learned, and challenges to be addressed by 6G technologies to enhance emergency response capabilities.