Not audio specific but…
Shelly products (smart relays, plugs, sensors, etc.) all work over local network control and I’ve been very happy with them. I have a bunch throughout the house, and they are all denied internet access at the network level.
Also, all HomeKit devices must, by the specification, allow local control. You should be able to use those devices locally using the Home Assistant HomeKit Device integration without having any Apple devices. My Ecobee thermostats work great through this integration even though they are also denied internet access.
Good luck, and have fun nerding out on your new home!
I think the answer largely depends on the devices you use. Many devices require an internet connection to integrate with HA. Fortunately, each HA integration should list whether or not they can work locally.
Here are some device suggestions:
Just as an example, I have Ecobee thermostats that are HomeKit compatible. Ecobee provides a cloud service, but I don’t use it at all, and my thermostats are denied internet access at the network level. They still work great through the HomeKit Devices integration.
Good luck!