If there is a way, I would have thought it would be via Home Assistant - using this to link the various aspects - I have all my various Fire TVs and Channels apps status in there, along with my IP cams (although I don't have Nest cams).
For example, it might be possible to detect something from a door bell in Home Assistant, then write some rules/scripts/automation to load an app on your device to play the video stream... assuming it can of course. Not directly in the app, but a round-about-way of achieving something similar.
It looks like Home Assistant can only grab still frames from Nest:
However, if there is an App on your device (whatever it is you use to watch Channels), chances are you could trigger a loading of that app, when someone is at the door/motion detected etc, if the Channels is playing a channel.
For me, Home Assistant is the glue that links the various aspects together.