So I am testing this out and getting an odd result. I blocked the Homepod and my phone from the internet, disconnected cellular. They are both on Wifi still so can talk to each other. Tested trying to stream music and they cannot get online.
On the homepod, Siri cannot seem to process homekit commands locally. It complained it could not get online. On my phone however, Siri was able to turn a light on/off pretty much instantly. I read some vauge info online and it sounds like the local processing of Homekit commands was added in iOS 16 which my phone has, but I have not seen any recent updates to the Homepod Mini so maybe it is coming to that soon?
While the voice command may need to be processed using an internet connection, once Siri knows what you want the command to HE will be local from the Homepod (or your phone) straight to the Hub. I definitely notice the difference in response time, Homekit is much faster than Alexa (which sends commands to HE via a cloud connection if I am not mistaken).
