Thank you for your screenshots and I could see the Searchbox.
I could to add Search box for Admin bar settings.
If you don't mind, please try the Develop version.
If you have activated the Jetpack plugin, Please note the name of the Search box is same.
Right menu search box: Jetpack search ( omni search )
Front menu search box: Search box that you said
If you have problems, Sorry please contact me again.