"Computer, dim lights by 30%"
"Computer, open curtains."
"Computer, vacuum the floor."
"Computer, play some jazz"
All of these are phrases are actual literal phrases that I use in my home, some on a daily basis. It can only be done, with current consumer tech, through the internet. All you need is a roomba, some 4$ smart bulbs, a spotify account, a 30$ auto curtain robot, and an alexa. For google home you can do the same but you can't call it a "computer."
In the future they will most likely be hooking up some LLM super computer to the home. In that case it can only be online.
The idealistic version of a smart home involves what we see in Star Trek TNG. Talking to the computer and only an online version of that can fulfill this vision currently and in the future. If you go offline, what you get is what I term a "programmable home" more than a "smart home".