feat: implement Paarrot API for Electron integration with navigation and IPC handlers

src/app/pages/client/ClientRoot.tsx

@@ -38,6 +38,7 @@ import { getFallbackSession } from '../../state/sessions';
 import { CallProviderWrapper } from '../../features/call/CallProviderWrapper';
 import { isTauriMobile, startBackgroundSync, stopBackgroundSync } from '../../utils/tauri';
 import { TitleBar } from '../../components/title-bar';
+import { initPaarrotAPI } from '../../paarrot-api';
 
 function ClientRootLoading() {
   return (
@@ -250,6 +251,13 @@ export function ClientRoot({ children }: ClientRootProps) {
   useVisibilitySync(mx);
   useBackgroundSync(mx);
 
+  // Initialize Paarrot API when client is ready
+  useEffect(() => {
+    if (mx) {
+      initPaarrotAPI(mx);
+    }
+  }, [mx]);
+
   useEffect(() => {
     if (loadState.status === AsyncStatus.Idle) {
       loadMatrix();