It's not very straight-forward, and you have to give the Google Home app access to your photos.
In the Google Home app on an iOS device, we can select our Google Nest Camera (Battery), select "History", select "Full History", select an event, select "Event Details", and then click on the small download icon in the upper right corner. The clip is then downloaded to our Photos. We cannot manually edit an event as we can in the Google Nest app.
Thank you for your feedback on this issue, I fully understand the frustrations of not having your new Nest Cams in the Nest App or available on https://bit.ly/3HtBgJC web app. I can imagine having to use two different apps at the moment is quite daunting, and could lead to frustration.
However, the new Nest cameras and doorbell are exclusive to the Home app because we wanted to create an integrated experience with your speakers and displays. A Nest Aware subscription applies to all of your cameras, speakers, and displays in the same home structure. Thank you for your continued patience, and support. I am more than happy to assist you further with this inquiry if you wish. Please let me know.