What I’m gathering is that “wave” can refer to a behavioral pattern that is substrate independent — it refers to a logical function more than it does an ontological presence

I think that's a good way of putting it.

As for what counts as a "substrate", I have no idea! In the old days, the idea of a substance that permeated seemingly-empty space was common. See: https://en.wikipedia.org/wiki/Aether_theories

Nowadays, the idea of aether has been discarded for the most part. But that said, there's still plenty we don't understand, like dark matter. There's no consensus on what dark matter is exactly; there are many competing theories. What we know is that there are observable phenomena that can't be explained without something that acts (roughly, at least) like matter in terms of its effect on gravity, but doesn't interact with electromagnetism like normal matter. That "something" is called dark matter, but its fundamental nature is an open question.