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I know there are a bunch of similar questions but I read through them all and they don't answer my question.

Let's say I give a box on a floor an initial "kick" of force such that it has kinetic energy $KE$. Due to friction between the box and the floor, the box will slide to a halt. This means the friction must supply work equal and opposite to the objects energy: $W = -KE$.

However, we know that friction is an irreversible process. This means there is an entropy increase $S > 0$. But according to the classical definition of entropy, $S = \frac{Q}{T}$. Since work does not appear in this equation, this would imply there had to be a heat transfer at some point, but where? Is the frictive force also causing heat?

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1) Work is done by the friction forces until the box stops.

2) Box kinetic energy is transformed to increased temperature (internal energy) of the sliding surfaces.

3) The cooling to the neighbourhood is an irreversible process, increasing entropy.

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This is an answer to the original title:

Is friction work or heat?

Neither work nor heat. Friction is a force:

Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other.2 There are several types of friction

In physics one has to be accurate in the use of terms, the units are different for force and for work. work and heat have the units of energy.

There is radiation in the work done with friction, because the electromagnetic interactions, end up as heat on the solid lattices., this link may help

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  • $\begingroup$ Right, and work is force times distance, and since the friction force was applied over a distance, it did work. $\endgroup$
    – gardenhead
    Jan 28, 2020 at 17:35
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You have mixed up many conepts here. In thermodynamics energy is added to the system through heat. Here you have added the energy via mechanical means. One thing is obvious, that most of the disspitative forces in one way or other produces heat. Now this heat produced due to dissipative forces increased the vibration and kinetic energy and thus entropy has increased. Don't take entropy as just a formula. Its much more than that. Do read thermodynamics concept thoroughly.

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Friccion supplies work, but usually this work cannot be stored as potential energy so the kinetic energy is basically dissipated into heat. The process is irreversible though, so you equation for the entropy does not apply.

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