Reconciling the drift velocity with Joule heating at high and low voltage

I’m trying to reconcile the particle behaviour in an electric field on the micro level with the conductor and the current properties on the macro level.

As far I understand – with resistance being constant an increase in voltage causes the power to increase and current flow to decrease. Also, an increase in voltage causes an increase in the drift velocity of the electrons.

The Joule heating happens because the drift velocity and electron-ion collisions cause the part of the energy of the electric field to be converted into the kinetic energy of the ions, and thus into thermal energy of the conductor.

To reduce these heat losses we increase the voltage applied to the conductor using transformers on the entry to a power line, and on the exit from it, like shown in this simple experiment.

On the macro level, the transformer increases the voltage applied to the conductor, and that allows using a thin wire that would overheat and melt when the same power would be drawn through it under lower voltage.

But surely on the micro level the increase in voltage will increase the electrons’ drift velocity and should increase the average number of collisions with ions and the total amount of energy transferred through those collisions, not decrease it. And given that the same conductor is used on low and high voltage – the total amount of electrons moving through the conductor would not change with the change of voltage, only their speed of movement.

So why does the Joule heating decreases when voltage goes up when it seems to have to increase?