The growing proliferation of Internet of Things (IoT) devices has intensified the need for sustainable energy solutions, particularly in resource-constrained deployments where non-rechargeable batteries and supercapacitors are the primary energy sources. Green IoT (G-IoT) frameworks address this challenge by combining energy-saving techniques with energy harvesting from ambient sources such as solar power. However, the intermittent nature of renewable energy and the non-ideal behavior of energy storage systems—such as energy leakage and capacity degradation—complicate reliable energy provisioning. This paper presents a novel Markovian framework for modelling the coupled dynamics of time-varying solar energy harvesting, time-dependent energy consumption, and state-dependent energy leakage in G-IoT systems. Unlike traditional steady-state models, our approach uses Discrete-Time Markov Chains (DTMCs) to capture the stochastic variability in both energy harvesting and consumption processes. We also introduce a refined leakage model in which the leakage rate is dynamically dependent on the stored energy level, enabling a more realistic characterization of energy losses due to energy leakage. Through extensive analytical evaluation, we examine how key parameters—such as storage capacity, leakage rate coefficient, and energy harvesting and consumption patterns—affect critical performance metrics, including the mean stored energy and energy-related service outage probability. Furthermore, we propose a parameter tuning strategy to optimize energy reliability and storage efficiency. The proposed model provides valuable insights for the design and optimization of robust, energy-aware IoT systems powered by renewable energy sources.