The language of setting an application type to “browser” is outdated and reflects a previous implementation of the system. You may find older documentation or articles by third parties still referring to this concept, but reality has changed.
If you want to set an application to what was once considered “browser” type: simply provide a URL in the placeholder callback URL field of the application. When a URL is in this field, your application is in browser mode. When there is no URL, it is not.