This paper investigates the integration of large-scale battery storage (LSBS) systems and power-to-gas (PtG) plants into a hybrid energy storage system. The study focuses on the combined operation of this system with a photovoltaic (PV) park. Multi-use applications are explored, including peak shaving, capacity firming, spot market trading, and continuous hydrogen production. A two-level hierarchical energy management concept is proposed to enhance technical and economic performance, integrated into a simulation framework to facilitate detailed end-of-life investigations. At the upper-level, a model predictive controller optimises trading on two spot markets. The controller incorporates short-term overload potential and ageing-aware operation of both the LSBS and the PtG plant. Battery ageing is modelled using a semi-empirical degradation model, with cost functions derived and piecewise linearised for mixed-integer linear optimisation. Electrolyser ageing is modelled using an equivalent operating hour model. At the lower-level, an adaptive power allocation strategy ensures grid power commitments despite PV power forecast errors. This lower-level control also reduces dynamic stress for both the battery and PtG plant, while ensuring continuous hydrogen production. A simulation of a typical summer day illustrates the developed energy management concept in detail. End-of-life simulations show that, compared to the standalone configuration, cost-equivalent hybridisation reduces PV curtailment by 8.0 to 12.1% and balancing group deviations by 0.77 to 0.85%. Further improvements from ageing-aware energy management increase profit by 8.8% and extend battery lifetime by 9.7%. Overall, the proposed hybridisation and energy management approach significantly enhance both technical performance and economic efficiency.