The Internet of Underwater Things (IoUT) supports marine sensing, environmental monitoring, subsea inspection, and autonomous underwater operations. However, IoUT communication is constrained by limited bandwidth, long propagation delay, time-varying underwater channels, intermittent connectivity, and strict energy budgets. Semantic Communication (SC) offers a promising alternative by transmitting task-relevant meaning rather than raw data, thereby improving communication efficiency in resource-constrained underwater networks. This paper presents a critical and feasibility-aware survey of SC for IoUT, focusing on opportunities, challenges, limitations, and future research directions. We first review the fundamentals of SC-enabled IoUT systems, including semantic representations, layered architectures, semantic channel modeling, and task-oriented evaluation metrics. We then examine learning-driven approaches based on machine learning (ML), knowledge graphs (KGs), vision-language models (VLMs), generative models, and federated learning (FL), with emphasis on their feasibility under underwater edge constraints. Representative applications, including environmental monitoring, marine ecology, subsea infrastructure inspection, disaster response, and autonomous underwater vehicle (AUV) coordination, are analyzed from an SC perspective. Finally, we identify key research directions involving standardized semantic models, reproducible testbeds, compute--communication trade-offs, trustworthy reconstruction, hybrid underwater links, energy-aware edge intelligence, semantic security, digital twins (DTs), and cross-domain interoperability. This survey provides a structured foundation for developing reliable, efficient, and meaning-driven IoUT communication systems.