Emit tool:sync socket event on skill state changes (#83)

* Refactor BillingPanel to use updated user usage structure

- Changed the usage data source in BillingPanel from activeTeam to user, aligning with the new IUserUsage interface.
- Updated the display of token usage percentage and progress bar to reflect the new usage metrics (spentThisCycleUsd and cycleBudgetUsd).
- Cleaned up commented-out code and improved layout for better readability and user experience.

* Enhance skill synchronization and connection status management

- Exported `deriveConnectionStatus` function from hooks for better accessibility.
- Introduced `syncToolsToBackend` function to synchronize tool states with the backend, ensuring up-to-date connection status.
- Integrated `syncToolsToBackend` calls in `SkillManager` lifecycle methods and socket connection events to maintain consistent state across the application.
- Added new `sync.ts` file to encapsulate synchronization logic, improving code organization and maintainability.

* Add Rust-side tool:sync emission and document dual socket codebase

Implement tool:sync on the Rust side so desktop/mobile apps emit skill
state to the backend natively, without relying on the frontend WebView.

- SocketManager: add sync_tools() method, derive_connection_status()
  helper, and sync_tools_via_channel() for event handler context
- SocketManager: emit tool:sync on "ready" (connect/reconnect)
- RuntimeEngine: store SocketManager reference, call sync_tools after
  start_skill, stop_skill, and auto_start_skills
- lib.rs: wire SocketManager into RuntimeEngine during setup
- CLAUDE.md: add Dual Socket Codebase pattern noting that any socket
  event change must be implemented in both TypeScript and Rust

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

---------

Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>

src/utils/tauriSocket.ts

@@ -16,6 +16,7 @@
 import { isTauri as coreIsTauri, invoke } from '@tauri-apps/api/core';
 import { listen, UnlistenFn } from '@tauri-apps/api/event';
 
+import { syncToolsToBackend } from '../lib/skills/sync';
 import { store } from '../store';
 import { setSocketIdForUser, setStatusForUser } from '../store/socketSlice';
 import { BACKEND_URL } from './config';
@@ -149,6 +150,10 @@ export async function setupTauriSocketListeners(): Promise<void> {
         const mappedStatus: ReduxStatus = statusMap[status] || 'disconnected';
         store.dispatch(setStatusForUser({ userId: uid, status: mappedStatus }));
         store.dispatch(setSocketIdForUser({ userId: uid, socketId: socket_id ?? null }));
+
+        if (mappedStatus === 'connected') {
+          syncToolsToBackend();
+        }
       }
     );