Graph Neural Networks (GNNs) have emerged as a powerful framework for modeling complex interconnected systems, hence making them particularly well-suited to address the growing challenges of next-generation Internet of Things (NG-IoT) networks. Existing studies remain fragmented, and there is a lack of comprehensive guidance on how GNNs can be systematically applied to NG-IoT systems. As NG-IoT systems evolve toward 6G, they incorporate diverse technologies. These advances promise unprecedented connectivity, sensing, and automation but also introduce significant complexity, requiring new approaches for scalable learning, dynamic optimization, and secure, decentralized decision-making. This survey provides a comprehensive and forward-looking exploration of how GNNs can empower NG-IoT environments. We commence by exploring the fundamental paradigms of GNNs and articulating the motivation for their use in NG-IoT networks. Besides, we intrinsically connect GNNs with the family of low-density parity-check codes, modeling the NG-IoT as dynamic constrained graphs. We highlight the distinct roles of node-, edge-, and graph-level tasks in tackling key challenges and demonstrate the GNNs' ability to overcome the limitations of traditional optimization. We examine the application of GNNs across core NG-enabling technologies and their integration with distributed frameworks to support privacy-preservation and distributed intelligence. We then delve into the challenges posed by adversarial attacks, offering insights into defense mechanisms. Lastly, we examine how GNNs can be integrated with emerging technologies. Our findings highlight the transformative potential of GNNs in improving efficiency, scalability, and security. Finally, we summarize the key lessons learned and outline promising future research directions, along with a set of design guidelines tailored for NG-IoT applications.