feat: Implemented FallbackAdapter for LLM

[KrishnaShuk]

Description

#868
This PR implements the FallbackAdapter for LLMs, bringing feature parity with the Python SDK. This component allows agents to automatically switch to backup LLM providers if the primary provider fails, times out, or becomes unavailable, ensuring high availability for production agents.

Python(agents) SDK code for fallback adapter: https://github.com/livekit/agents/blob/main/livekit-agents/livekit/agents/llm/fallback_adapter.py

Changes Made

• Created packages/agents/src/llm/FallbackAdapter.ts implementing the FallbackAdapter and FallbackLLMStream classes.
• Implemented Priority Failover: Accepts a list of LLMs and attempts them in order.
• Implemented Active Health Check: Background recovery logic that uses the actual ChatContext to verify when a failed provider has recovered (instead of a simple timer).
• Implemented State Tracking: Emits llm_availability_changed events when providers go down or recover.
• Implemented Glitch Protection: Respects retryOnChunkSent to prevent the agent from repeating partial sentences if a stream fails mid-generation.
• Exported the new adapter in packages/agents/src/llm/index.ts.

Pre-Review Checklist

• Build passes: All builds (lint, typecheck, tests) pass locally
• AI-generated code reviewed: Removed unnecessary comments and ensured code quality
• Changes explained: All changes are properly documented and justified above
• Scope appropriate: All changes relate to the PR title, or explanations provided for why they're included
• Video demo: N/A (Backend logic change, verified via Unit Tests)

Testing

• Automated tests added/updated
• All tests pass (8 tests covering initialization, failover, total failure, events, and stream delegation)
• Make sure both restaurant_agent.ts and realtime_agent.ts work properly (This change is additive/opt-in and does not affect existing agents unless configured to use the adapter)

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Latest commit: 7595a17

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