In, at least Milano and Oxygen, as far as I could see, mobile display does not offer any positions in the header/menu area except for Logo and mobile menu. Just as a suggestion for your future templates, it would be nice, especially for multi language sites, to be able to put the language switcher in the mobile header. To show users that it is a multi-language site. And, as modal search does not work in the mobile menu, maybe a search field. I found a very nice example for the search field on mobiles at: https://www.geberit.de/de/
(Sorry, it's in German).