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It’s been a while since I setup my system, but as I recall they are interconnected via the smart hub, and do not need internet at all. When I first configured our system, IOT was probably the topic of an exploratory whitepaper and not yet reliant on internet. But times have changed! Give it a bit more searching; we’ve been happy for quite a long time with the devices. They even have plugs which you can convert dumb devices to a smart HA device—but you’ll have to get them on eBay because they’ve been discontinued:/

Caseta switches can handle 3-pole switches in exactly the way you’ve described. You could even set them up with dimmers, pico remotes (and eliminate one of the switches). If you get the wireless bridge (now known as Smart Hub) you might be able to tie it into your HA depending on your ecosystem.