feat: quick capture sends to chat instead of quick-capture endpoint

Replace POST /api/quick-capture with: create a conversation, send the
message, and fire-and-forget the SSE generation stream so the assistant
processes the request in the background without blocking the UI.
The new conversation appears immediately in the chat tab.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

lib/app.dart

@@ -5,21 +5,17 @@ import 'package:go_router/go_router.dart';
 import 'package:flutter_timezone/flutter_timezone.dart';
 
 import 'core/constants.dart';
-import 'core/exceptions.dart';
 import 'core/theme.dart';
 import 'providers/api_client_provider.dart';
 import 'providers/auth_provider.dart';
-import 'providers/capture_queue_provider.dart';
 import 'providers/capture_work_queue_provider.dart';
 import 'providers/briefing_provider.dart';
 import 'providers/calendar_provider.dart';
 import 'providers/chat_provider.dart';
 import 'providers/knowledge_provider.dart';
 import 'providers/news_provider.dart';
-import 'providers/notes_provider.dart';
 import 'providers/settings_provider.dart';
 import 'providers/update_provider.dart';
-import 'providers/tasks_provider.dart';
 import 'screens/auth/login_screen.dart';
 import 'screens/briefing/briefing_screen.dart';
 import 'screens/knowledge/knowledge_screen.dart';
@@ -516,12 +512,6 @@ class _QuickCaptureBar extends ConsumerStatefulWidget {
 class _QuickCaptureBarState extends ConsumerState<_QuickCaptureBar> {
   final _controller = TextEditingController();
 
-  @override
-  void initState() {
-    super.initState();
-    WidgetsBinding.instance.addPostFrameCallback((_) => _drainOfflineQueue());
-  }
-
   @override
   void dispose() {
     _controller.dispose();
@@ -537,36 +527,6 @@ class _QuickCaptureBarState extends ConsumerState<_QuickCaptureBar> {
     ref.read(captureWorkQueueProvider.notifier).enqueue(text);
   }
 
-  Future<void> _drainOfflineQueue() async {
-    if (!mounted) return;
-    final queue = ref.read(captureQueueProvider);
-    if (queue.isEmpty) return;
-    final api = ref.read(quickCaptureApiProvider);
-    for (final text in List<String>.from(queue)) {
-      if (!mounted) break;
-      try {
-        final result = await api.capture(text);
-        // Dequeue before the mounted check — SharedPreferences doesn't need
-        // the widget alive, and skipping this would leave a ghost item.
-        await ref.read(captureQueueProvider.notifier).dequeue(text);
-        if (!mounted) break;
-        switch (result.type) {
-          case 'note':
-            ref.invalidate(notesProvider);
-          case 'task':
-          case 'todo':
-            ref.invalidate(tasksProvider);
-        }
-      } on NetworkException {
-        break;
-      } catch (_) {
-        // Server error or unexpected failure — drop from queue to prevent
-        // ghost items that can never be cleared.
-        await ref.read(captureQueueProvider.notifier).dequeue(text);
-      }
-    }
-  }
-
   Future<void> _toggleCaptureMic() async {
     final voice = ref.read(voiceProvider);
     if (voice.voiceModeActive) {
@@ -596,10 +556,8 @@ class _QuickCaptureBarState extends ConsumerState<_QuickCaptureBar> {
   @override
   Widget build(BuildContext context) {
     final location = GoRouterState.of(context).matchedLocation;
-    final offlineQueueCount = ref.watch(captureQueueProvider).length;
     final workQueue = ref.watch(captureWorkQueueProvider);
     final isWorking = workQueue.isNotEmpty;
-    final totalPending = workQueue.length + offlineQueueCount;
 
     // Show snackbar when a result is published.
     ref.listen(captureResultProvider, (_, result) {
@@ -634,12 +592,7 @@ class _QuickCaptureBarState extends ConsumerState<_QuickCaptureBar> {
                       isDense: true,
                       contentPadding: const EdgeInsets.symmetric(
                           horizontal: 14, vertical: 10),
-                      prefixIcon: totalPending > 0
-                          ? Badge(
-                              label: Text('$totalPending'),
-                              child: const Icon(Icons.cloud_upload_outlined),
-                            )
-                          : isWorking
+                      prefixIcon: isWorking
                               ? const Padding(
                                   padding: EdgeInsets.all(12),
                                   child: SizedBox(