Providing timely and informative data in integrated terrestrial and non-terrestrial networks is critical as data volume grows while the resources available on devices remain limited. To address this, we adopt a semantics-aware approach to optimize the Version Age of Information (VAoI) in a status update system in which a remote Energy Harvesting (EH) Internet of Things (IoT) device samples data and transmits it to a network of interconnected Low Earth Orbit (LEO) satellites for dissemination and utilization. The optimal update policy is derived through stochastic modeling and optimization of the VAoI across the network. The results indicate that this policy reduces the frequency of updates by skipping stale or irrelevant data, significantly improving energy efficiency.