How to measure energy stored in a battery

Total Energy stored in the capacitor, = QV/2 = 0.5 CV^2

where,

Q = amount of charge stored when the whole battery voltage appears across the capacitor.

V= voltage on the capacitor proportional to the charge.

Then, energy stored in the battery = QV

Half of that energy is dissipated in heat in the resistance of the charging pathway, and only QV/2 is finally stored on the capacitor.

We cannot say that Q=0 because as soon as you connect the battery in series with the parallel plate capacitor, it starts charging the capacitor. But if you say that Q=0 , this implies that there is no battery.

Initial charge, Q = 0 means that time before you connect the battery, say at t=0, the charge on the capacitor is zero.

Generally battery charge controllers have a minimum voltage drop between the input and the charge output to the battery this should be found in the specifications of the charge controller. It is unlikely that you will meet this condition by connecting the input to the pwm charger to the output of the Victron mppt.