The script very nicely dismounts the dmg and even moves it to the trash, but it creates a second version of the app with a new name. You end up with two versions of Brave in your applications folder. Unfortunately, when you launch the newer version: “Brave Browser.app”, your history, bookmarks etc. are not there. If you go back to the applications folder and launch the old version: “Brave.app”, all of your information is there.
The new version doesn’t give you a way to import history and bookmarks from the old version, but only from other browsers.