You can use the Apple Watch to control the music on the HomePod with the “Now Playing” app but why wouldn’t you just use the HomePod Siri to control music on the HomePod?
But you want to play music there? Lol. Most people play music in the room they’re occupying. If you think Apple’s solution to this issue you’ve created yourself is to buy more HomePods, then I don’t know what to tell ya.
Nobody here is an Apple software engineer that works on Siri so don’t expect a definitive answer. I can tell you though that not all Siri is created equal. Ask Siri on the HomePod what your heart rate is and see what you get back. Each Siri is tailored to work on its own specific device.
Here’s a little hint to get what you want to work. It involves an app called Shortcuts.