Implemented phase 1 for the POC prototype in the Website service.

Services/Website/Sources/Library/Internal/Components/SiteHeader.swift

@@ -10,6 +10,9 @@ struct SiteHeader: HTML {
     /// The format marked as current in the navigation, or `nil` for none.
     let active: Format?
 
+    /// The text the search field is filled with, or `nil` to leave it empty.
+    let query: String?
+
     /// The signed-in viewer, or `nil` to render the signed-out actions.
     let viewer: Viewer?
 
@@ -18,12 +21,15 @@ struct SiteHeader: HTML {
     /// Creates a site header.
     /// - Parameters:
     ///   - active: the format marked as current, or `nil` (the default) for none.
+    ///   - query: the text the search field is filled with, or `nil` (the default) to leave it empty.
     ///   - viewer: the signed-in viewer, or `nil` (the default) to render the signed-out actions.
     init(
         active: Format? = nil,
+        query: String? = nil,
         viewer: Viewer? = nil
     ) {
         self.active = active
+        self.query = query
         self.viewer = viewer
     }
 
@@ -159,6 +165,7 @@ private extension SiteHeader {
                 .id("site-search-query"),
                 .type(.search),
                 .name("q"),
+                .value(query ?? ""),
                 .placeholder("Search title, issue, grade or shop")
             )
             button(