Disproving the existence of a medium with certain expected properties and behaviours - one of which was that light travelled through it like waves through water.
The reality is that light travels through spacetime and has completely unexpected and non-intuitive properties, one of which is an absolutely constant velocity.
This doesn't mean spacetime isn't a medium of some kind, it means spacetime isn't a medium of any familiar or intuitive kind, and the old waves-on-water metaphor is too simple to explain it.
QFT suggests spacetime is filled with fields of all kinds and particles are excitations of these fields.
But what these "fields" actually are, and what they're made of, and why there are certain kinds of fields and not others, and why they operate with relativistic geometry, is a complete mystery.
Proving/disproving the existence of a medium was the whole point of the Michaelson-Morley experiment.