The colors of the search window that opens when you click the search icon in the header are part of the theme's header colors. In the page editor, go to Global theme styles > Header colors > Overlay window and change Background. The same group also holds the text and link colors of that window.
These colors are shared by all overlay screens of the header, such as the language selection and quick contact screens, so they always match. Click Publish changes at the top right once you are done.