The browser will download and attempt to apply updates while using the browser or while its closed. The browser will not be fully updated though until the updates are downloaded, installed and the browser is restarted.
However, I am a little confused about what some of you all are saying. Can anyone please clarify the specific notification they’re referring to? Do you mean the update notification on the main menu that appears in the browser here?
Or the update notification that appears on the About Brave page here?
Or a different notification all together?