It also depends on what /you/ setup - eg, you can certainly control some things locally and some things only through the cloud if you are using the manufacturer

It also depends on what /you/ setup - eg, you can certainly control some things locally and some things only through the cloud if you are using the manufacturers hub, but most things you can also buy a zwave stick and/or a zigbee stick and connect to your devices directly. Some are a perpetual cat and mouse game though for the companies that simply must snoop your data as part of their biz model or have another reason to be terrified of you directly talking to their things. And like any smart thing you put in your house, some things you need to block at the DNS level if they are hardwired to phone home constantly. But yes, Home Assistant and choosing the right things makes it possible to keep everything internal for sure