The thermal storage value represents the thermal energy that is stored as thermal mass in the walls, floors and interior objects of your model. The energy balance is calculated with the assumption that the heat gain in your building (+ values) is balanced out by the heat loss in your building (- values). This is because the mechanical heating/cooling system will supply energy in the correct proportions to maintain the balance, or thermal equilibrium of your building. In practice, when you add up all the components from the EP Results component, it’s usually not balanced by a small amount, which is the small amount of heat that is trapped in as thermal mass, and is not accounted for in any of the EnergyPlus outputs. Hence it is calculated after the simulation in the component. Specifically is calculated as the difference between your gains and losses. In your case, the reason why it is so large, is because your gains and losses are significantly unbalanced.
The reason they’re unbalanced, is the real problem here. They’re unbalanced because the Read EP Results components outputs the electrical/gas energy (the work) used to supply heating/cooling energy, not the actual thermal energy. The ratio of thermal energy to work is not equivalent. For heating systems, that ratio can be around 0.8, for cooling systems it can be 3 or 5. In your case, you have a very high ratio for cooling, which is why your cooling load is so low, which in turn is computing a high thermal storage component to try and (incorrectly) balance the loads.
For these reasons, the heat balance component can’t be used with HVAC systems, you have to use it with a ideal air loads system, which is essentially an ‘idealized’ HVAC system that has a one to one ratio of work to energy. You can view your HVAC systems-based energy breakdown using just the monthly bar chart.