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>
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2026-03-25 20:30:41 +05:30
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