feat(proxy): implement per-app takeover mode

Replace global live takeover with granular per-app control:
- Add start_proxy_server command (start without takeover)
- Add get_proxy_takeover_status to query each app's state
- Add set_proxy_takeover_for_app for individual app control
- Use live backup existence as SSOT for takeover state
- Refactor sync_live_to_provider to eliminate code duplication
- Update ProxyToggle to show status per active app

src/types/proxy.ts

@@ -38,6 +38,12 @@ export interface ProxyServerInfo {
   started_at: string;
 }
 
+export interface ProxyTakeoverStatus {
+  claude: boolean;
+  codex: boolean;
+  gemini: boolean;
+}
+
 export interface ProviderHealth {
   provider_id: string;
   app_type: string;