That's true for a steady-state wave, and hence this model is accurate for a steady-state light wave. But if you were to consider short pulses of light then ther

That's true for a steady-state wave, and hence this model is accurate for a steady-state light wave. But if you were to consider short pulses of light then there is no longer a relationship between the group velocity and phase velocity. The group velocity of these pulses through a medium will still be lower than the speed of light in a vacuum and phase kicks won't influence the group velocity. Explaining how the group velocity of light can be slower in a medium than in a vacuum requires analyzing the coupling of photons with electrons to form polariton quasiparticles. You can then calculate the mass of these polaritons which in turn gives you the speed and get the full picture. Doing this, however, is incredibly complex and so it's much easier to consider simplified scenarios like either the steady-state case where you can simply reason about the scenario in terms of interference patterns between the light wave and the electromagnetic waves produced by oscillating electrons, or you can consider some non-steady state scenarios involving photons themselves being absorbed and reemitted by electrons but neither of these explanations fully capture the phenomenon.