When a battery is connected to a resistance circuit, we know that it loses energy because heat is emitted as a result of the collisions between the electrons and stuff, but my question is, is the change in kinetic energy of the electrons zero or negligible?
The voltage difference between the poles of the battery creates an electric field that pushes the electrons to the positive electrode. If there would be no resistance, the electrons would thus accelerate while moving from one electrode to the other and their kinetic energy would be increasing as they move.
However, because of collisions in the resistor the electrons lose energy. The individual electrons continuously change direction due to these collisions and lose energy while doing so. On average however, the electrons move with a constant velocity through the resistor.
The drude model is the classical way to describe this behavior.
is the change in kinetic energy of the electrons zero or negligible?
It is negligible, but not zero. The Fermi velocity in a typical conductor is approximately 1500 km/s while the drift velocity is approximately 0.2 um/s, which is 13 orders of magnitude smaller. Since the kinetic energy is proportional to the square of the velocity this means that the KE due to the current’s drift velocity is around 26 orders of magnitude smaller than the baseline Fermi KE of the electrons.