refactor: centralise user timezone as a standalone setting

Browser timezone is now synced to user_settings["user_timezone"] on
every login/page load (App.vue). The briefing scheduler and LLM context
both read from this single source, falling back to the legacy
briefing_config.timezone for existing users during migration.

- App.vue: PUT /api/settings with browser IANA timezone on startAppServices
- routes/chat.py: fall back to stored user_timezone when not sent in request
- briefing_scheduler: read user_timezone setting; briefing_config.timezone
  kept as fallback only
- routes/briefing.py: pass tz_override from user_timezone to live-patched scheduler
- Remove timezone field from BriefingConfig interface and all briefing UI

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

frontend/src/App.vue

@@ -8,7 +8,7 @@ import { useShortcuts } from "@/composables/useShortcuts";
 import { useAuthStore } from "@/stores/auth";
 import { useChatStore } from "@/stores/chat";
 import { useSettingsStore } from "@/stores/settings";
-import { apiGet } from "@/api/client";
+import { apiGet, apiPut } from "@/api/client";
 
 useTheme();
 
@@ -22,6 +22,8 @@ const { showShortcuts, toggleShortcuts, closeShortcuts } = useShortcuts();
 function startAppServices() {
   chatStore.startStatusPolling();
   settingsStore.fetchSettings();
+  // Sync browser timezone to the server on every login/page load.
+  apiPut("/api/settings", { user_timezone: Intl.DateTimeFormat().resolvedOptions().timeZone }).catch(() => {});
 }
 
 function stopAppServices() {