Electrode Potential at Equilibrium
From paragraph of textbook.
At the electrode-electrolyte interface the metal ions in electrolyte leak out, leaving a negative charge on electrode side of interface. While metal ions migrate at the other side of the interface from the electrolyte solution.
This eventually comes to a stop when the equilibrium is reached. That is the rate of negative charge build-up is equal to the positive charge. Like you say at this point there is no more drive for the reaction to go one way or the other.
However, now because of the charge separation at the interface, there is a potential difference between both sides of this interface which leads to the reduction potential we read out which is not zero. This is where the Nernst equation comes in handy.