With Google's new 2-app solution, you should be able to see the video feeds for ALL of your cameras and doorbells in the Google Home app, but you can't administer them there. You can see video feeds in the Google Home app either by selecting the individual camera or doorbell or by clicking the "Cameras" icon at the top of the initial screen.
However, from posts I've seen about the new Google Nest Doorbell (Battery), it doesn't have a "Live" feed all the time because it's battery-powered (even when wired). When you select your Google Nest Doorbell (Battery) in the Google Home app, does it show as "Idle"? And do you have a "Live video" option? That's how our new Google Nest Camera (Battery) shows when it's not plugged in, and we then have to select the "Live video" option in order to activate the camera and see the live video feed.
I agree, I have the first gen nest camera's and just assumed the newer gen would allow me to view my new camera through my browser. I use that feature more then viewing my camera's on my phone. Dang, If I had know this I would not of bought another nest camera. Why would google with endless development resources not have that available for gen 2 camera's. Even if its not at home.nest.com, it should still should be available somewhere. Come on google, your losing customers.
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