The voltage is able to create an electric field. This represents a change in potential over some distance ($V/m$). The effect of an electric field therefore depends not only on the strength, but on the distance over which it can act.
While the field might provide a force to charges (like free electrons), it will have almost no effect on an atom. The change in the field over the size of the atom is so small that the electron cloud orientation is not affected. So the field can't energize the individual atoms.
how is it possible that not all emitted electrons have the same kinetic energy?
The ejection is a messy process. Imagine having a device that can deliver a very precise "kick" to a ball. You place a ball on it and it will always kick the ball up exactly 2 meters. Now you take the device into a ball pit. Sometimes you get the maximum KE into a single ball and it goes up 2m into the air. Sometimes it goes a bit sideways and doesn't reach 2m. Sometimes the ball hits another and just shuffles some balls around.
What you can say is that you never see any ball go higher than 2m. The same thing into the photoelectric experiment. By turning up the voltage, it's like squashing down how high the balls can go. The idea is to find the maximum extent, not the proportion of ejections that reach that extent.