feat(intelligence): complete migration to Rust backend

- Unify all intelligence modules to use intelligenceClient
- Delete legacy TS implementations (agent-memory, reflection-engine, heartbeat-engine, context-compactor, agent-identity, memory-index)
- Update all consumers to use snake_case backend types
- Remove deprecated llm-integration.test.ts

This eliminates code duplication between frontend and backend, resolves
localStorage limitations, and enables persistent intelligence features.

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

desktop/src/store/connectionStore.ts

@@ -24,8 +24,6 @@ import {
   type LocalGatewayStatus,
 } from '../lib/tauri-gateway';
 import {
-  performHealthCheck,
-  createHealthCheckScheduler,
   type HealthCheckResult,
   type HealthStatus,
 } from '../lib/health-check';
@@ -165,6 +163,8 @@ export const useConnectionStore = create<ConnectionStore>((set, get) => {
     localGateway: getUnsupportedLocalGatewayStatus(),
     localGatewayBusy: false,
     isLoading: false,
+    healthStatus: 'unknown',
+    healthCheckResult: null,
     client,
 
     // === Actions ===