fix(web): center nav in window + Library link + Search placeholder

Three operator-reported issues:

- Header was flex with the nav inside a flex-1 span — when the
  right side (search + user menu) grew wider than the left
  (wordmark), the nav's centered position drifted off page-center.
  Switched to grid-cols-3 with justify-self-{start,center,end} so
  the middle column pins to true window-center regardless of side
  widths.
- Library nav link pointed to /library, which 308-redirects via
  +page.server.ts. Operator reported it didn't navigate. Linked the
  nav button directly to /library/artists so SPA navigation skips
  the redirect roundtrip. matchPrefix='/library' keeps isActive
  matching every Library tab.
- SearchInput placeholder was 'Search artists, albums, tracks…' —
  shortened to 'Search' and added a Lucide Search icon inside the
  input on the left. Padding adjusted (pl-7) so the input text
  clears the icon.

web/src/lib/components/SearchInput.svelte

@@ -2,6 +2,7 @@
   import { page } from '$app/state';
   import { goto } from '$app/navigation';
   import { untrack } from 'svelte';
+  import { Search } from 'lucide-svelte';
 
   let value = $state(page.url.searchParams.get('q') ?? '');
   let timeout: ReturnType<typeof setTimeout> | null = null;
@@ -51,12 +52,20 @@
   }
 </script>
 
-<input
-  type="search"
-  placeholder="Search artists, albums, tracks…"
-  aria-label="Search"
-  bind:value
-  oninput={onInput}
-  onkeydown={onKey}
-  class="w-full max-w-md rounded border border-border bg-surface px-3 py-1 text-sm focus-visible:outline focus-visible:outline-2 focus-visible:outline-accent"
-/>
+<label class="relative block w-full max-w-md">
+  <Search
+    size={14}
+    strokeWidth={1.5}
+    aria-hidden="true"
+    class="pointer-events-none absolute left-2 top-1/2 -translate-y-1/2 text-text-secondary"
+  />
+  <input
+    type="search"
+    placeholder="Search"
+    aria-label="Search"
+    bind:value
+    oninput={onInput}
+    onkeydown={onKey}
+    class="w-full rounded border border-border bg-surface pl-7 pr-3 py-1 text-sm focus-visible:outline focus-visible:outline-2 focus-visible:outline-accent"
+  />
+</label>

web/src/lib/components/Shell.svelte

@@ -36,9 +36,9 @@
     goto('/login', { replaceState: true });
   }
 
-  function isActive(href: string): boolean {
-    if (href === '/') return page.url.pathname === '/';
-    return page.url.pathname.startsWith(href);
+  function isActive(prefix: string): boolean {
+    if (prefix === '/') return page.url.pathname === '/';
+    return page.url.pathname.startsWith(prefix);
   }
 
   // Primary nav. Sits centered in the top bar (replaces the prior left
@@ -46,22 +46,33 @@
   // destinations, plus Library acting as a parent for Artists / Albums /
   // Liked / History / Playlists (tabs at /library/+layout.svelte).
   // Search + user menu live on the right side of the header (unchanged).
+  // Library targets the Artists tab directly so SPA navigation doesn't
+  // bounce through the /library 308-redirect. isActive('/library')
+  // still matches all sub-routes by prefix so the active state covers
+  // every tab.
   const navItems = [
-    { href: '/',          label: 'Home',     icon: House },
-    { href: '/library',   label: 'Library',  icon: LibraryBig },
-    { href: '/discover',  label: 'Discover', icon: Compass }
+    { href: '/',                 label: 'Home',     icon: House,       matchPrefix: '/' },
+    { href: '/library/artists',  label: 'Library',  icon: LibraryBig,  matchPrefix: '/library' },
+    { href: '/discover',         label: 'Discover', icon: Compass,     matchPrefix: '/discover' }
   ];
 </script>
 
 <svelte:window onclick={handleWindowClick} onkeydown={(e) => e.key === 'Escape' && (menuOpen = false)} />
 
 <div class="grid h-screen grid-rows-[auto_1fr_auto] bg-background text-text-primary">
-  <header class="flex items-center gap-3 md:gap-6 border-b border-border bg-surface px-3 md:px-4 py-2">
-    <a href="/" class="font-semibold text-sm md:text-base whitespace-nowrap">{appName()}</a>
+  <!-- 3-col grid so the middle column (nav) is centered on the page
+       regardless of how wide the side columns are. With the prior
+       flex+justify-center layout the nav's "available space" shifted
+       whenever search or the user menu grew, so the nav drifted off
+       window-center. Grid pins each column to a fixed lane. -->
+  <header class="grid grid-cols-3 items-center border-b border-border bg-surface px-3 md:px-4 py-2 gap-3 md:gap-6">
+    <a href="/" class="font-semibold text-sm md:text-base whitespace-nowrap justify-self-start">
+      {appName()}
+    </a>
 
-    <nav aria-label="Primary" class="flex flex-1 items-center justify-center gap-1 md:gap-2">
+    <nav aria-label="Primary" class="flex items-center justify-center gap-1 md:gap-2 justify-self-center">
       {#each navItems as item}
-        {@const active = isActive(item.href)}
+        {@const active = isActive(item.matchPrefix)}
         <a
           href={item.href}
           class="group flex items-center gap-2 rounded px-2 md:px-3 py-2 min-h-[44px]
@@ -76,6 +87,7 @@
       {/each}
     </nav>
 
+    <div class="flex items-center gap-3 md:gap-6 justify-self-end min-w-0">
     <div class="hidden md:block min-w-0 max-w-xs flex-shrink">
       <SearchInput />
     </div>
@@ -133,6 +145,7 @@
         </div>
       {/if}
     </div>
+    </div>
   </header>
 
   <!-- Subtle 1200x600 radial highlight at the top of the scroll