Google Nest devices don’t run Android and don’t have web browsers, so you can’t access an openHAB UI or install the app. However, you can control any devices that are exposed to Google Assistant using the screens. I never do that though, since I can just use voice commands.
Personally, I don’t see value in wall-mounted screens as control interfaces. If I want to control something by touch, I already have my phone and tablets that are just as easy, if not easier, to pick up. I have an old Android phone on the wall running Habpanel, but it’s purely to convey information at a distance.