Language switcher widget in header area for Travelify theme

This theme uses a different template setup, so you have to add your code inside header-extensions.php that you can find in travelify folder >> library >> structure. If you add code inside header.php it is possible to make language switched only above (like in your case) or below header area but not right in it.

Another option is to get this done via Child Theme and here is an example with search bar but with some tweaking you can make it work with your widget as well.