The emerging demands of sixth-generation wireless networks, such as ultra-connectivity, native intelligence, and cross-domain convergence, are bringing renewed focus to cooperative non-orthogonal multiple access (C-NOMA) as a fundamental enabler of scalable, efficient, and intelligent communication systems. C-NOMA builds on the core benefits of NOMA by leveraging user cooperation and relay strategies to enhance spectral efficiency, coverage, and energy performance. This article presents a unified and forward-looking survey on the integration of C-NOMA with key enabling technologies, including radio frequency energy harvesting, cognitive radio networks, reconfigurable intelligent surfaces, space-air-ground integrated networks, and integrated sensing and communication-assisted semantic communication. Foundational principles and relaying protocols are first introduced to establish the technical relevance of C-NOMA. Then, a focused investigation is conducted into protocol-level synergies, architectural models, and deployment strategies across these technologies. Beyond integration, this article emphasizes the orchestration of C-NOMA across future application domains such as digital twins, extended reality, and e-health. In addition, it provides an extensive and in-depth review of recent literature, categorized by relaying schemes, system models, performance metrics, and optimization paradigms, including model-based, heuristic, and AI-driven approaches. Finally, open challenges and future research directions are outlined, spanning standardization, security, and cross-layer design, positioning C-NOMA as a key pillar of intelligent next-generation network architectures.