Here's a funny thing. Until recently, my HomePod would respond to "Hey Siri, play Radio New Zealand National" by playing RNZ National via Tune-In. Last week (before the 13.3 update) that stopped working, and Siri started defaulting to an Apple Music station.
I wondered whether they'd done something to the Tune-In tie-in, or to NZ based HPs (since they're not officially available here), but it turns out that I now need to be a bit more specific: "Hey Siri, play radio station Radio New Zealand National" is the new magic phrase, and even though it's a bit of a mouthful, it's still quicker than launching the RNZ app on my phone and Airplaying it to the Pod...