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/components/settings/SettingsPage.tsx

@@ -177,8 +177,8 @@ export function SettingsPage({
 
   const {
     isRunning,
-    startWithTakeover: startProxy,
-    stopWithRestore: stopProxy,
+    startProxyServer,
+    stopWithRestore,
     isPending: isProxyPending,
   } = useProxyStatus();
   const [failoverEnabled, setFailoverEnabled] = useState(true);
@@ -186,9 +186,9 @@ export function SettingsPage({
   const handleToggleProxy = async (checked: boolean) => {
     try {
       if (!checked) {
-        await stopProxy();
+        await stopWithRestore();
       } else {
-        await startProxy();
+        await startProxyServer();
       }
     } catch (error) {
       console.error("Toggle proxy failed:", error);