Well, it seems pretty clear to me. During the steady-state running, the average input power is always greater than the average output power. This is easy to see simply by inspection of the average power traces. This difference in power represents losses in the system, probably mostly in the mosfets and the coil resistances.
Only after the power supply is turned off is there some "excess" energy delivered in the output, since the output power decays to zero over a few of milliseconds while the input power is zero. Integrating this power curve from the time of power-off to the end gives a value for this "excess" energy. The fact that the power decays to zero represents, again, losses that are not overcome.
During the startup phase before steady-state is reached, the input power is quite a bit greater than the output power. Again, integrating both input and output power curves from the time of power-on to the time of steady-state gives a value for the respective energies, and shows that the input energy during this time is quite a bit greater than the output energy. This difference represents energy stored in the system, along with the inevitable losses.
The "excess" energy after turn off is only about 1/3 of the difference between input and output at the startup.
So it seems to me that the simplest explanation is that the system is storing some energy that was delivered in the startup transients, and returning some small part of this stored energy after power-off. During steady-state the input power is a little greater than the output power, during startup some energy is stored, after shut-down some of the stored energy is released to the output. You get out what you put in, minus losses.
If one chooses to consider only the power in the primary tank as "input", that is, by measuring the voltage and current at the L1 coil terminals (by doing a differential voltage measurement Vecap2-Vecap to obtain the voltage across the coil for example) one sees that this power, in the hundreds of VA, is almost perfectly reactive and actually represents a small amount of stored energy sloshing back and forth between the coil and the capacitor, with losses being replaced by the power supply during steady-state operation, a tiny amount making it across to the secondary, finally to give it all up after power is turned off.
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