At some point this all kind of drifts apart from ontic science and starts to become a matter of narrative or interpretation, but I would generally agree with that.
Waves are mathematically-friendly possible configurations of the underlying system.
It's mathematically valid to choose the most convenient configurations for analysis because the systems are (pretty) linear, so we can just project any actual state into a sum of wave states, apply our mathematical model, and add it all back to get the new real state.
A lot of physical phenomena are composed of pretty predictable distributions of wave states, so projecting from a realistic state to a sum of wave states is usually straightforward enough.
For example, a moving particle looks like the sum of a bunch of waves all closely grouped around a particular wavelength.
Waves are mathematically-friendly possible configurations of the underlying system.
It's mathematically valid to choose the most convenient configurations for analysis because the systems are (pretty) linear, so we can just project any actual state into a sum of wave states, apply our mathematical model, and add it all back to get the new real state.
A lot of physical phenomena are composed of pretty predictable distributions of wave states, so projecting from a realistic state to a sum of wave states is usually straightforward enough.
For example, a moving particle looks like the sum of a bunch of waves all closely grouped around a particular wavelength.