There is already a search box in wordpress dashboard for posts, products, pages etc. in their listing page.
My client use wordpress admin with their phone so he requested another search box on top of those pages with the same functionality. I can edit codes if I need to, but I don't know where to start. Have anybody needed that kind of behavior before? It seems easy but I don't know how to edit listing pages in wordpress dashboard.
position
parameter it moves back to the top where you're hoping. I know this doesn't answer your question but it may work as an alternative