Maybe ‘Google Assistant’ would have been more correct. Because it looks like Home Assistant is referencing an API?
But if an openHAB integration doesn’t exist, that’s not relevant at the moment. I didn’t want to point out it’s not there, because I’m not capable of making it myself, so that would be a pointless statement.
But I wanted to make sure that such an integration doesn’t exist, rather than not knowing about it.
As fas as I know, Google Home does not expose any devices integrated with it and makes them controllable from other services. Maybe they’ve added one in the last little bit.
It might be possible to do something via Matter too, I’ve not looked down that path. But I don’t have any direct experience with that. I know you can go the other direction by exposing OH stuff to Google Home via Matter (as long as you have a Google device that supports Matter).