I added the shortcode to insert the icon in the top bar header. When you click it, the input field struggles to open and stays behind the search icon. I want it to work like it does on your website where the input pops out to the left over the other items on the page.
For that, try the following settings: https://i.imgur.com/3lx85pN.png
This will place the search to an absolute position, where it is removed from the document flow. The closest relative parent will be the “anchor” point for the search position then. You may have to play around with the “top” and “right” position values to get the correct alignment, but this is the setup we use in our demo header search.