The integration of Terrestrial and Non-Terrestrial Networks (TN-NTNs), introduced in 5G, is advancing toward a unified and seamless network of networks in Sixth-Generation (6G). This evolution markedly increases the volume of generated and exchanged data, imposing stringent technical and operational requirements along with higher cost and energy consumption. Consequently, efficient management of data generation and transmission within this unified architecture has become essential. Inthis article, we investigate semantics-aware information handling in unified TN-NTNs, where data communication between distant TN nodes is enabled via an NTN. We consider an Internet of Things (IoT) monitoring system in which status updates from a remote Energy Harvesting (EH) device are delivered to a destination monitor through a network of Low Earth Orbit (LEO) satellites. We leverage semantic metrics, such as Query Version Age of Information, which collectively capture the timeliness,relevance, and utility of information. This approach minimizes the transmission of stale, uninformative, or unusable information, thereby reducing the volume of data that must be transmitted and processed. The result is a substantial reduction in energy consumption and data exchange within the network—achieving up to 73% lower energy-charging requirements and fewer transmission demands than the state of the art—without compromising the conveyed information.