Would increasing separation of terminals of a battery increase potential differnce?

If my understanding is correct, the chemical reaction in a battery is basically a conveyor belt that moves electrons from the positive to the negative terminal of the battery until the electric field between the terminals slows the rate of the reaction to zero.

If this is true, would the electric potential difference between the terminals then be given by the electric field between the terminals multiplied by the distance between them (assuming the electric field between them is constant)?

And if so, then would separating the terminals further increase the potential difference?

I feel like this is incorrect though because it would increase the potential energy stored in the battery which I thought was a constant value determined by the chemicals in the reaction, but if the electric field is the only thing slowing the reaction I don’t see why separating the terminals should have any effect since it wouldn’t change the electric field (again assuming the battery was designed similar to a capacitor in that the electric field between the terminals remained constant at every point between them).