feat: LiveKit AI answering agent (Gemini 2.5 Flash native audio)

- Hospital receptionist agent "Helix" with Gemini realtime speech-to-speech
- Tools wired to platform: lookupDoctor, bookAppointment, collectLeadInfo, transferToAgent
- Loads hospital context (doctors, departments) from platform GraphQL on startup
- Connects to LiveKit Cloud, joins rooms when participants connect
- Silero VAD for voice activity detection
- @livekit/agents + @livekit/agents-plugin-google + @livekit/agents-plugin-silero

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

package.json

@@ -23,6 +23,9 @@
     "@ai-sdk/anthropic": "^3.0.58",
     "@ai-sdk/openai": "^3.0.41",
     "@deepgram/sdk": "^5.0.0",
+    "@livekit/agents": "^1.2.1",
+    "@livekit/agents-plugin-google": "^1.2.1",
+    "@livekit/agents-plugin-silero": "^1.2.1",
     "@nestjs/common": "^11.0.1",
     "@nestjs/config": "^4.0.3",
     "@nestjs/core": "^11.0.1",
@@ -34,7 +37,8 @@
     "ioredis": "^5.10.1",
     "reflect-metadata": "^0.2.2",
     "rxjs": "^7.8.1",
-    "socket.io": "^4.8.3"
+    "socket.io": "^4.8.3",
+    "zod": "^4.3.6"
   },
   "devDependencies": {
     "@eslint/eslintrc": "^3.2.0",