Think of the battery as providing potential energy (electric field) rather than kinetic energy (electrons flow).
When a depletion region is created due to the diffusion of electrons and holes across the PN junction, the depletion region becomes an insulator across which there is no motion of any carriers (holes or electrons). So the depletion regions is essentially an Open Circuit. Applying more reverse potential increases the width or size of this depletion region or open circuit. So no electrons or holes reach the battery terminals. If the reverse potential increases hgh enough, the insulator is catastrophically destroyed and carriers can breach this insulator. This is reverse breakdown.
In forward bias conditions, the depletion region width is reduced. If reduced far enough, the insulator disappears and current can flow under the influence of the external electric field.