I already pointed that out a few days ago.
Its worth getting as many as possible to pick a few inverter transformers apart to study the windings.
Most put the secondary & rectifier in series with the base winding (that's why the HT is usually negative) when the capacitor is discharged, the secondary charging current pulses are added to the base winding to increase the pulsed collector current, as the capacitor reaches full charge the current pulses due to the secondary diminish, leaving only the base bias resistor to sustain oscillation.
That produces rapid recharge after a flash but economises battery drain while the flash is at the ready for the next picture.