On all these new additions, the button works the same. One press launches the assistant, while double-tapping gives you a visual insight of your day. The press will still turn it up with a kind of walkie talkie that will keep listening for orders until you leave.
There's nothing to hide why Google is pressing for this button: it's about winning the AI support wars. Access to a Google Assistant is the easiest, the more likely you could use over Alexa Alexa and other competitors. That could, in turn, be convinced to buy smart-aided Assisted devices that can be transmitted to the Google ecosystem.