As I've written in the other comment, the Home Assistant Operating System is useless without an Internet connection. It has to pull the Docker images since it doesn't have any version of the images at all.
This thing isn't as private and as local as it is claimed to be. It's very tied to services provided by Nabu Casa, including the very visible cloud integration of theirs. They've expanded it now to backups.
Yes, there are resources loaded from the Internet. The map tiles are loaded from a third party in the initial setup and every time you view the map. Icons are loaded from https://brands.home-assistant.io/. https://github.com/home-assistant/frontend/issues/18549 is the issue.
This thing isn't as private and as local as it is claimed to be. It's very tied to services provided by Nabu Casa, including the very visible cloud integration of theirs. They've expanded it now to backups.