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/api/client.ts

@@ -329,7 +329,6 @@ export interface BriefingConfig {
   slots: BriefingSlots;
   notifications: boolean;
   temp_unit: 'C' | 'F';
-  timezone: string;
 }
 
 export interface BriefingFeed {
@@ -364,7 +363,6 @@ const DEFAULT_BRIEFING_CONFIG: BriefingConfig = {
   slots: { compilation: true, morning: true, midday: false, afternoon: false },
   notifications: true,
   temp_unit: 'C',
-  timezone: '',
 };
 
 export async function getBriefingConfig(): Promise<BriefingConfig> {