Anything with gas loading or heat after death.
From the beginning with gas loading; after switching off with heat after death. Sometimes, cells are switched on again after a period of heat after death. That is not always the end of the experiment.
Also, there are many cases where the COP exceeded 3 with input power.
No, you don't have to take that into account. Nearly all of the energy consumed by electrolysis comes out of the cell immediately. You don't need to account for it because it is already accounted for. Energy is never stored, except in tiny amounts of palladium deuteride, which is easy to measure as an endothermic reaction when the gas is stored, and as an exothermic reaction when the palladium de-gasses. The two always balance out to zero. The absolute total amount of possible storage is easily computed. It is thousands of times smaller than the excess heat in most cases.
In a control experiment with Pd-H, the heat balance is zero; there is never excess heat (except the small endothermic and exothermic reactions listed above, which balance out to zero). Heat input with electrolysis before excess heat appears is like the heat used to manufacture the glassware. It is gone by the time the excess heat begins.
Could you provide links to the papers about the "cases where the COP exceeded 3 with input power", or titles of these papers ?