Hi Phil,
I think this may be what you’re looking for. Siri actually has its own volume that is separate from the HomePod Mini content volume. (Turn off auto volume then turn Siri volume all the way down - I think that will give you no audible Siri confirmations)
How to change Siri volume - Apple Support
”Change Siri's volume on your HomePod
You can ask Siri to speak louder, quieter, or at a specific volume. Say "Hey Siri," then say something like:
- "Speak louder."
- "Always speak quieter."
- "Set your volume to sixty percent."
HomePod automatically adjusts Siri's response volume based on the level of noise in the room, your distance from HomePod, and how loudly you're speaking to Siri. You can turn automatic volume on or off by saying, "Hey Siri, turn on automatic Siri volume," or "Hey Siri, turn off automatic Siri volume."”