As said above, I’ve heard it used since I was a kid usually in the way ** pulykamell** describes. For Example: “Switch to WKRP. What channel?”
As noted by several posters, it seems likely (though maybe not conclusively so) that it’s the fact that traditional radio stations’ new competitors – streaming services, satellite radio – tend to use the term “channel.” Marketers of “terrestrial” radio stations, trying to make their stations feel contemporary to their listeners, likely have started to adopt the “channel” terminology to match those newer competitors.