It sounds like you're asking for a feature that’s available on the Ring doorbell but not on the Google Nest Doorbell. Specifically, the ability for the display hub to automatically show the live feed when an activity zone is triggered. Currently, with the Nest Doorbell, you have to manually press the doorbell or view it through the app to see the live video, even when an activity zone is alerted. This is a feature many users have requested, as it would be very convenient for the hub to automatically display live video when someone walks into view. Unfortunately, this feature isn’t available right now, but it’s possible that Google could add it in a future update based on user feedback. In the meantime, you can still receive motion alerts from the Nest Doorbell when activity zones are triggered, though it won't automatically show on the hub. Hopefully, Google will take this into consideration and add the feature soon!
