The generate_menu_bar_items hook allows you to hook non-menu item elements such as buttons, icons and whatever else your design requires. Content added there will automatically display in the navigation and mobile header.
Using a Hook Element
If you have GP Premium, you can use a hook element and add the content like this:
Using a Function
If you are using the free GeneratePress theme, you can use the PHP snippet method:
add_action( 'generate_menu_bar_items', function() {
?>
<?php
} );