fix(search): route the library header search to /search

Typing in the desktop header search bar ran library.search() in place and
relied on /library rendering the results inline. On every other /library/**
route nothing rendered them, so the search bar looked broken: results were
fetched and never shown.

Make /search the single surface that renders results. The header bar becomes a
navigator — it hands the query and route-derived scope to /search via ?q= and
?scope=, which seed the page and run the search on arrival. The inline result
block and the header's scope chips are removed; the chips live on /search,
which owns the results. The empty `all` scope is omitted from the URL, and
typing while already on /search does not push a history entry per keystroke.

src/routes/library/+page.svelte

@@ -12,8 +12,9 @@
   // Scroll guard from layout - prevents accidental taps during scrolling (Android)
   const scrollGuard = getContext<ReturnType<typeof useScrollGuard>>("scrollGuard");
 
-  let searchResults = $derived($library.searchResults);
-  let searchQuery = $derived($library.searchQuery);
+  // Search results are rendered exclusively by /search — this page used to
+  // render them inline, which made the header search bar appear broken on every
+  // other /library/** route. TRACES: UR-049 | DR-063
 
   const isMusicLibrary = $derived($currentLibrary?.collectionType === "music");
 
@@ -169,28 +170,7 @@
 </script>
 
 <div class="space-y-8">
-  {#if searchQuery}
-    <!-- Search results -->
-    <div>
-      <div class="flex items-center justify-between mb-4">
-        <h1 class="text-2xl font-bold text-white">
-          Search results for "{searchQuery}"
-        </h1>
-        <button
-          onclick={() => library.clearSearch()}
-          class="text-sm text-gray-400 hover:text-white"
-        >
-          Clear search
-        </button>
-      </div>
-
-      <LibraryGrid
-        items={searchResults}
-        loading={$isLibraryLoading}
-        onItemClick={handleItemClick}
-      />
-    </div>
-  {:else if showInlineLibraryContent}
+  {#if showInlineLibraryContent}
     <!-- Library content (live TV / channels / other inline-rendered types) -->
     <div class="space-y-6">
       <div class="flex items-center gap-4">