I ran the UI and didn't load anything from external source.

The Internet should only needed to download the image. You could download and flash it manually. The setup shouldn't require the Internet. What needed the Internet?

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.

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.

My internet was out today and I couldn't even log in to the local UI.