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/+layout.svelte

@@ -6,8 +6,12 @@
   import { library } from "$lib/stores/library";
   import { useScrollGuard } from "$lib/composables/useScrollGuard";
   import Search from "$lib/components/Search.svelte";
-  import SearchScopeChips from "$lib/components/search/SearchScopeChips.svelte";
-  import { resolveSearchScope, type SearchScope } from "$lib/utils/searchScope";
+  import {
+    resolveSearchScope,
+    searchRouteUrl,
+    shouldNavigateToSearch,
+    type SearchScope,
+  } from "$lib/utils/searchScope";
   import AppHeader from "$lib/components/AppHeader.svelte";
   import BottomUi from "$lib/components/BottomUi.svelte";
   import SleepTimerModal from "$lib/components/player/SleepTimerModal.svelte";
@@ -48,18 +52,22 @@
     }
   });
 
+  // The header bar is a *navigator*, not a second results surface: /search is
+  // the only route that renders searchResults, so searching here routes there
+  // with the query + route-derived scope in the URL. Previously this ran
+  // library.search() in place, which was invisible on every /library/** page
+  // except /library itself.
+  // TRACES: UR-049 | DR-063
   async function handleSearch(query: string) {
-    if (query.trim()) {
-      await library.search(query, searchScope);
-    } else {
+    if (!query.trim()) {
       library.clearSearch();
+      return;
     }
-  }
-
-  async function handleScopeChange(next: SearchScope) {
-    searchScope = next;
-    if (searchQuery.trim()) {
-      await library.search(searchQuery, next);
+    if (shouldNavigateToSearch($page.url.pathname, query)) {
+      await goto(searchRouteUrl(query, searchScope));
+      // The query now lives in the URL; clear the header input so returning to
+      // a library page does not leave a stale term sitting in the box.
+      searchQuery = "";
     }
   }
 </script>
@@ -74,14 +82,12 @@
     <AppHeader search={librarySearch} />
 
     {#snippet librarySearch()}
+      <!-- Scope chips live on /search, which owns the results. -->
       <Search
         bind:value={searchQuery}
         placeholder="Search your library..."
         onSearch={handleSearch}
       />
-      {#if searchQuery.trim()}
-        <SearchScopeChips scope={searchScope} onChange={handleScopeChange} />
-      {/if}
     {/snippet}
 
     <!-- Main content. The BottomUi below is an in-flow flex sibling, so this