Many real-time applications of the Internet of Things (IoT) need to deal with correlated information generated by multiple sensors. The design of efficient status update strategies that minimize the Age of Correlated Information (AoCI) is a key factor. In this paper, we consider an IoT network consisting of sensors equipped with the energy harvesting (EH) capability. We optimize the average AoCI at the data fusion center (DFC) by appropriately managing the energy harvested by sensors, whose true battery states are unobservable during the decision-making process. Particularly, we first formulate the dynamic status update procedure as a partially observable Markov decision process (POMDP), where the environmental dynamics are unknown to the DFC. In order to address the challenges arising from the causality of energy usage, unknown environmental dynamics, unobservability of sensors' true battery states, and large-scale discrete action space, we devise a deep reinforcement learning (DRL)-based dynamic status update algorithm. The algorithm leverages the advantages of the soft actor-critic and long short-term memory techniques. Meanwhile, it incorporates our proposed action decomposition and mapping mechanism. Extensive simulations are conducted to validate the effectiveness of our proposed algorithm by comparing it with available DRL algorithms for POMDPs.