feat(desktop): mirror a pending update into the tray (cinny-desktop #6)

While an update is available the web client asks the native side to show
"Restart to update (vX)" in the tray menu and an "update ready" tooltip;
it's cleared once a check reports we're current, and kept while
installing or after a failed attempt. Clicking the tray item runs the
same install flow as the toast, so progress and failures show in-app.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01PPmy3tPq869XDW4njjVaKA

src/app/pages/client/ClientNonUIFeatures.tsx

@@ -68,7 +68,7 @@ import { useReminders } from '../../hooks/useReminders';
 import { getRoomRetentionMs, isExpired } from '../../utils/retention';
 import { useTauriUpdateProgress, useTauriUpdater } from '../../hooks/useTauriUpdater';
 import { isNetworkUpdateError } from '../../utils/updateErrors';
-import { invokeTauri, isTauri as isTauriApp } from '../../hooks/useTauri';
+import { invokeTauri, isTauri as isTauriApp, useTauriEvent } from '../../hooks/useTauri';
 import { TauriDesktopFeatures } from '../../components/TauriDesktopFeatures';
 import { KeyboardShortcutsDialog, useKeyboardShortcutsTrigger } from '../../features/shortcuts';
 import { useRoomsListener } from '../../hooks/useRoomsListener';
@@ -965,6 +965,24 @@ function TauriUpdateFeature() {
     });
   }, [status, setToast, installFromToast]);
 
+  // [cinny-desktop #6] Mirror a pending update into the tray ("Restart to
+  // update" + tooltip) so a dismissed toast isn't the only reminder. Kept while
+  // installing or after a failed attempt (the update is still pending); cleared
+  // once a check says we're current.
+  useEffect(() => {
+    if (!isTauri) return;
+    if (status.state === 'available') {
+      invokeTauri('set_tray_update_ready', { version: status.version });
+    } else if (status.state === 'up-to-date') {
+      invokeTauri('set_tray_update_ready', { version: null });
+    }
+  }, [isTauri, status]);
+
+  useTauriEvent('lotus-tray-install-update', () => {
+    if (firedRef.current) dismissToast(`tauri-update-${firedRef.current}`);
+    installFromToast();
+  });
+
   return null;
 }