Hi,
Can you please add temporary back-end and FTP details, so I can take a look at the imported settings? Thank you!
I checked the header search – while I cannot see the elementor options, but one of the hidden via custom CSS, which I suppose is generated via Elementor itself. It is unrelated to the plugin, so you might have to ask the elementor support about that, or check the options again and clear the site cache to make sure it is populated.