feat: sync device timezone to backend on startup

On shell mount, reads the IANA timezone from the device via
flutter_timezone and POSTs it to PUT /api/settings as user_timezone.
Mirrors the web app's App.vue behaviour so briefing events and the
chat route use the correct local time on Android.

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

lib/app.dart

@@ -2,6 +2,8 @@ import 'package:flutter/material.dart';
 import 'package:flutter_riverpod/flutter_riverpod.dart';
 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';
@@ -159,19 +161,29 @@ class _ShellState extends ConsumerState<_Shell> {
   @override
   void initState() {
     super.initState();
-    // Silent update check — only if we haven't already checked this session.
-    // Skipping when status is not idle/error prevents the dialog from
-    // re-appearing every time the shell re-mounts (e.g. after visiting settings).
     WidgetsBinding.instance.addPostFrameCallback((_) {
+      // Silent update check — only if we haven't already checked this session.
       final repoUrl = ref.read(forgejoRepoUrlProvider);
-      if (repoUrl == null || repoUrl.isEmpty) return;
-      final status = ref.read(updateProvider).status;
-      if (status == UpdateStatus.idle || status == UpdateStatus.error) {
-        ref.read(updateProvider.notifier).check(repoUrl);
+      if (repoUrl != null && repoUrl.isNotEmpty) {
+        final status = ref.read(updateProvider).status;
+        if (status == UpdateStatus.idle || status == UpdateStatus.error) {
+          ref.read(updateProvider.notifier).check(repoUrl);
+        }
       }
+      // Sync device timezone to backend so briefing and chat use local time.
+      _syncTimezone();
     });
   }
 
+  Future<void> _syncTimezone() async {
+    try {
+      final tzInfo = await FlutterTimezone.getLocalTimezone();
+      await ref.read(settingsApiProvider).syncTimezone(tzInfo.identifier);
+    } catch (_) {
+      // Best-effort — failure is non-critical.
+    }
+  }
+
   int _tabIndex(String location) {
     for (var i = 0; i < _tabs.length; i++) {
       if (location.startsWith(_tabs[i])) return i;

lib/data/api/settings_api.dart

@@ -0,0 +1,13 @@
+import 'package:dio/dio.dart';
+
+class SettingsApi {
+  const SettingsApi(this._dio);
+  final Dio _dio;
+
+  Future<void> syncTimezone(String ianaTimezone) async {
+    await _dio.put<void>(
+      '/api/settings',
+      data: {'user_timezone': ianaTimezone},
+    );
+  }
+}

lib/providers/api_client_provider.dart

@@ -10,6 +10,7 @@ import '../data/api/milestones_api.dart';
 import '../data/api/notes_api.dart';
 import '../data/api/projects_api.dart';
 import '../data/api/quick_capture_api.dart';
+import '../data/api/settings_api.dart';
 import '../data/api/tasks_api.dart';
 import '../data/repositories/auth_repository.dart';
 import '../data/repositories/chat_repository.dart';
@@ -85,3 +86,7 @@ final milestonesRepositoryProvider = Provider<MilestonesRepository>((ref) {
 final briefingApiProvider = Provider<BriefingApi>((ref) {
   return BriefingApi(ref.watch(dioProvider));
 });
+
+final settingsApiProvider = Provider<SettingsApi>((ref) {
+  return SettingsApi(ref.watch(dioProvider));
+});