feat(web): mount SearchInput in Shell header

Header grows a flex-1 column between the brand and the user menu.
Existing Shell tests remain green (the search input has no impact on
nav/menu behavior).

web/src/lib/components/Shell.svelte

@@ -4,6 +4,7 @@
   import { user, logout } from '$lib/auth/store.svelte';
   import { player } from '$lib/player/store.svelte';
   import PlayerBar from './PlayerBar.svelte';
+  import SearchInput from './SearchInput.svelte';
 
   let { children } = $props<{ children: import('svelte').Snippet }>();
 
@@ -30,8 +31,11 @@
 <svelte:window onclick={() => (menuOpen = false)} onkeydown={(e) => e.key === 'Escape' && (menuOpen = false)} />
 
 <div class="grid h-screen grid-cols-[auto_1fr] grid-rows-[auto_1fr_auto] bg-background text-text-primary">
-  <header class="col-span-2 flex items-center justify-between border-b border-border bg-surface px-4 py-3">
+  <header class="col-span-2 flex items-center gap-4 border-b border-border bg-surface px-4 py-3">
     <div class="font-semibold">Minstrel</div>
+    <div class="flex-1">
+      <SearchInput />
+    </div>
     <div class="relative">
       <button
         type="button"