Voice systems only require Internet because companies have designed them that way to keep you on the hook and collecting your data. There’s no reason that voice control can’t run on a local box except for this business decision. Voice control systems had been around for years before everything was in the cloud, and with the advances made in the technology since then, the accuracy would be just fine on a local system.

I don't know any that are for sale on the internet but the deep learning, mesh network and microcontroller tech to join together such a capability are readily available and open source.

I thought Apple's system didn't use the internet. The voice recognition happens on the phone. No?

Even having a separate, but integrated, internet-connected voice recognition system would allow the devices themselves not to be internet-connected.

This is possible on Android, you can have an Android app call out to Google for voice control, and have the app control your local network.

You can make your own.