feat(websearch): add Grok CLI support and improve install guidance

- Add Grok CLI detection (grok-4-cli by lalomorales22) alongside Gemini CLI
- Add WebSearch health check group to health-service.ts
- Update settings UI to show both Gemini and Grok CLI providers
- Add detailed install hints when no WebSearch CLI is installed
- Update API routes to return grokCli status
- Both CLI and dashboard users now see clear installation guidance

Providers:
- Gemini CLI: FREE tier (1000 req/day), no API key needed
- Grok CLI: Requires xAI API key (XAI_API_KEY), web + X search

src/cliproxy/cliproxy-executor.ts

@@ -28,6 +28,7 @@ import {
 import { isAuthenticated } from './auth-handler';
 import { CLIProxyProvider, ExecutorConfig } from './types';
 import { configureProviderModel, getCurrentModel } from './model-config';
+import { getWebSearchHookEnv } from '../utils/websearch-manager';
 import { supportsModelConfig, isModelBroken, getModelIssueUrl, findModel } from './model-catalog';
 import {
   findAccountByQuery,
@@ -43,7 +44,7 @@ import {
   ensureMcpWebSearch,
   installWebSearchHook,
   displayWebSearchStatus,
-} from '../utils/mcp-manager';
+} from '../utils/websearch-manager';
 
 /** Default executor configuration */
 const DEFAULT_CONFIG: ExecutorConfig = {
@@ -386,10 +387,14 @@ export async function execClaudeWithCLIProxy(
   // 7. Execute Claude CLI with proxied environment
   // Uses custom settings path (for variants), user settings, or bundled defaults
   const envVars = getEffectiveEnvVars(provider, cfg.port, cfg.customSettingsPath);
-  const env = { ...process.env, ...envVars };
+  const webSearchEnv = getWebSearchHookEnv();
+  const env = { ...process.env, ...envVars, ...webSearchEnv };
 
   log(`Claude env: ANTHROPIC_BASE_URL=${envVars.ANTHROPIC_BASE_URL}`);
   log(`Claude env: ANTHROPIC_MODEL=${envVars.ANTHROPIC_MODEL}`);
+  if (Object.keys(webSearchEnv).length > 0) {
+    log(`Claude env: WebSearch config=${JSON.stringify(webSearchEnv)}`);
+  }
 
   // Filter out CCS-specific flags before passing to Claude CLI
   const ccsFlags = [