Zigbee is local and if you really wanted to you can use Home Assistant 100% offline it will be just neutered and basic.

I run home automation with lights, switches, outlets, heaters and some more and not a single device has internet access. They all use Zigbee (a simple radio protocol) to talk to homeassistant which is open source and hosted on a machine that lives under my desk.

Separating tasks between the dehumidifier and outlet has the advantage that each individual device can be a lot simpler, leaving less attack surface. My power outlet can't read the humidity sensor, it doesn't need to talk to an external server, it doesn't even need to know that the thing connected to it is a dehumidifier. It's just a chip that receives a radio signal and toggles a relay on or off. That's it.

Separating the two concerns also lets me replace the devices separately if one breaks or my requirements change. If I suddenly need wifi or bluetooth instead of Zigbee or if it's for some reason no longer supported by homeassistant, I can just replace a 9€ outlet instead of the whole dehumidifier that could get bricked by the proprietary app losing support.