If you take the perspective that "work is the increase in total mechanical energy of a system", then there really no work being done. The potential energy is just being converted to kinetic energy (of some sort). It's not really correct to say that " total kinetic energy (translational and rotational) is mgh". It would be more correct to say that any increase in kinetic energy:

$$E[total] = E[translationa]+E[rotational] = \frac{1}{2}mv^2+\frac{1}{2} I \omega^2 $$

is associated with an equal decrease in $$mgh =E[potential]$$.

If you define work only as the increase in kinetic energy and then compare the dynamics of a high-friction system (with increases in both translational and rotational energy, no-slip system to a no-friction one ( with only increases in translational kinetic energy since there is no torque on the cylinder), you might infer that the frictional surface is "doing the work" that is causing the increase in angular velocity.

If you take the perspective that "work is the increase in total mechanical energy of a system", then there really no work being done. The potential energy is just being converted to kinetic energy (of some sort). It's not really correct to say that " total kinetic energy (translational and rotational) is mgh". It would be more correct to say that any increase in kinetic energy:

$$E[total] = E[translationa]+E[rotational] = \frac{1}{2}mv^2+\frac{1}{2} I \omega^2 $$

is associated with an equal decrease in $$mgh =E[potential]$$.

So it's the exchange of potential energy for kinetic energy that is doing hte work. The incline is just a constraint that limits the path over which this exchange takes place in position. Friction is actually causing an increase in heat energy. It is a "dissapative" exchange of potential energy for thermal energy.