A base station (BS) transmits updates to users over a fading broadcast channel (BC) using nonorthogonal multiple access (NOMA). It accumulates energy from external sources in a finite-capacity, non-ideal battery experiencing charging and discharging losses proportional to their powers. Our goal is to minimize the long-term average Version Age of Information (VAoI) across all users, subject to power constraints, by optimizing charging duration, charging power, discharging power, and user scheduling. VAoI is defined as the number of versions the receiver lags behind the source. We solve this using a Markov Decision Process (MDP) with value iteration and find that: (i) optimal charging duration and power can be determined via a convex optimization problem; and (ii) if it is optimal to transmit to a user at a given VAoI, it remains optimal at higher VAoIs when other parameters are constant. We also propose a drift-plus-penalty (DPP) based solution. Additionally, we benchmark an offline policy with non-causal knowledge of energy, data packet arrivals, and channel power gains. Numerical simulations show that MDP and DPP-based policies outperform the benchmark greedy policy. Furthermore, comparing with downlink Time Division Multiple Access (TDMA), we find NOMA superior when packet arrival rates and energy availability are higher. This work is an extension of [1], which considers AoI minimization over an energy harvesting point-to-point fading channel with non-ideal batteries, to an energy harvesting downlink fading broadcast channel with the metric of version age of information using non-orthogonal multiple access.