We investigate the optimal power control for multisensor estimation of correlated random Gaussian sources. A group of wireless sensors obtains local measurements and transmits them to a remote fusion center (FC), which reconstructs the measurements using the minimum mean-square error estimator. All the sensors are equipped with an energy harvesting module and a transceiver unit for wireless, directed energy sharing between neighboring sensors. The sensor batteries are of finite storage capacity and prone to energy leakage. Our aim is to find optimal power control strategies, which determine the energies used to transmit data to the FC and shared between sensors, so as to minimize the long-term average distortion over an infinite horizon. We assume centralized causal information of the harvested energies and channel gains, which are generated by independent finite-state stationary Markov chains. The optimal power control policy is derived using a stochastic predictive control formulation. We also investigate the structure of the optimal solution, a Q-learning based suboptimal power control scheme and two computationally simple and easy-to-implement heuristic policies. Extensive numerical simulations illustrate the performance of the considered policies.