feat(F-065): completed feature

project/frontend/src/app/search/page.tsx

@@ -42,6 +42,7 @@ export default async function SearchPage({ searchParams }: Props) {
         </h1>
         <form method="GET" action="/search" className="flex gap-3">
           <input
+            id="search-page-q"
             name="q"
             type="search"
             defaultValue={query}

project/frontend/src/components/layout/Header.tsx

@@ -186,6 +186,8 @@ export function Header() {
               <div className="relative w-full">
                 <input
                   type="search"
+                  id="site-search"
+                  name="q"
                   value={q}
                   onChange={(e) => handleSearchChange(e.target.value)}
                   onFocus={() => { if (q.trim() && (results.length > 0 || suggestions.length > 0)) setShowDropdown(true); }}