On basis of that, I'd be more likely to say "QM needs to describe everything as a wave, and sometimes certain kinds of localized 'wave-packets' move around coherently, and that's what we'd call 'particles'". That also seems to gel with less coherent states where it feels like there's not really a particle to be found.

So, I'm curious why you'd prefer to relate the eigenstates themselves as particles. Again in the oscillator case, the eigenstates themselves seem less coherent and seem to behave less classically than I'd hope.

My best guess is that the property those states have that is not as well replicated by the "particle as a coherent wave packet phenomenon" is that they have well-defined energy quanta. But that's just a bit of a stab in the dark here. It perhaps makes more sense from the perspective of "particles are the things that we're able to measure in detectors" POV, though.