Just downloading the Omniverse Launcher AppImage and running it, doesn’t allow you to log in. It lets you authenticate in a browser window, but then tries to launch a url scheme that has not been registered.
Simply copy the URL from your browser, and in another terminal window, go to the directory where you put the launcher, and paste the url after the name of the AppImage:
$ ./omniverse-launcher-linux.AppImage 'omniverse-launcher://login?state=...