Do kinetic energy and inductor energy violate conservation of energy?
Voltage and current are emergent approximations, not fundamental things. If you want to bring the velocities of electrons into consideration, then you have to understand what's going on at the quantum mechanical level. Which is hard work.
Working with I and V requires ignoring the electron behaviour, just as working with pressure, which is also an emergent approximation, requires ignoring individual atoms' velocities and sizes. While pressure and volume are well approximated over a wide range of values, the finite size of atoms causes pressure to deviate from the simple linear laws at very high pressure, and the finite velocities cause (for instance) muzzle velocities to be limited in guns that use expanding gases as a driver.
It turns out that using I and V as if they are fundamental works very well over many more orders of magnitude than do the gas laws approximate the behaviour of gases.
In practice, the L is inferred from energy measurements, so you could consider that any small electronic contribution to energy is already accounted for.