I need to use a NavigationView because I need a search box there.

This is a sample code, very basic.

@State var searchText = ""

var body: some View {
    NavigationView {
      List {
        NavigationLink(destination: Color(.red) ) {
          Text("aaa")
        }
        NavigationLink(destination: Color(.red) ) {
          Text("bbb")
        }
        NavigationLink(destination: Color(.red) ) {
          Text("ccc")
        }
      }

    }
    .searchable(text: $searchText, prompt: "search...")
    .navigationBarTitle("", displayMode: .inline)
    .edgesIgnoringSafeArea(.top)

    .navigationBarHidden(true)
}

Look at the annoying area at the top (I have colored it yellow on Photoshop for reference).

How do I get rid of this area and move the search box up?

I'm not sure but I think it has to do with

    .navigationBarTitle("", displayMode: .inline)

does it help to remove that line?

Nope, no difference at all.

if you enable .navigationBarHidden , there is no more search, so how this solved your problem?