I think that it does not need a separate area of the screen reserved for searching, but that there should be an explicit way to indicate that you want to search

I think that it does not need a separate area of the screen reserved for searching, but that there should be an explicit way to indicate that you want to search. For example, this could be a popup window. Unlike the URL, which it is useful to be displayed even if you are not entering a new URL, this is not necessary for entering search queries, so using a popup window for this purpose may be helpful.