feat(flutter/home): home screen with five sections

Sections mirror the web home: Recently added · Rediscover (albums +
artists) · Most played · Last played artists. Tap routes pushed for
albums/artists; track-tap is wired in the player task. Pull-to-refresh
re-fetches /api/home.

flutter_client/lib/shared/routing.dart

@@ -5,6 +5,7 @@ import 'package:go_router/go_router.dart';
 import '../auth/auth_provider.dart';
 import '../auth/login_screen.dart';
 import '../auth/server_url_screen.dart';
+import '../library/home_screen.dart';
 import 'widgets/version_gate.dart';
 
 GoRouter buildRouter(Ref ref) {
@@ -30,7 +31,7 @@ GoRouter buildRouter(Ref ref) {
       ShellRoute(
         builder: (ctx, state, child) => VersionGate(child: _ShellWithPlayerBar(child: child)),
         routes: [
-          GoRoute(path: '/home', builder: (_, __) => const _HomePlaceholder()),
+          GoRoute(path: '/home', builder: (_, __) => const HomeScreen()),
         ],
       ),
     ],
@@ -51,9 +52,3 @@ class _ShellWithPlayerBar extends StatelessWidget {
   }
 }
 
-class _HomePlaceholder extends StatelessWidget {
-  const _HomePlaceholder();
-  @override
-  Widget build(BuildContext context) =>
-      const Scaffold(body: Center(child: Text('Home — coming in Task 14')));
-}