Why do power requirement figures for water electrolysis on the web seem to be wrong?
They said it right, "... requires at least 241.8 kJ ..." . You just found that one can simply calculate the molar formation enthalpy from the cell voltage, and vice versa, those two informations are redundant.

Of course you cannot run the electrolysis at the minimum voltage, because it will be extremely slow! You would just balance the electrochemical potential of the cell (created by the reverse reaction as soon as you make a small amount of hydogen and oxygen).

To make any actual electrolysis, you need a higher voltage, and the difference is converted into heat at the internal ohmic resistance of your cell. The minimum additional voltage is called the cell overvoltage, below that you don't get electrolysis. It is necessary to be able to break through the polarised electrolyte layers at the electrodes. So you cannot get towards 100% efficiency by running very slow.