Partially Support updateChatCtx with Phonic plugin.

[qionghuang6]

Description

This PR adds additional support for updateChatCtx with the Phonic plugin.
There are 2 use cases in mind:

• Rehydrating a conversation with chat history when a RealtimeSession begins: For this use case, in situations where the config message has not yet been sent to Phonic, we include the conversation history's text content along with the roles involved as part of the system_prompt appendum being sent over to Phonic.
• Adding system or developer messages to the conversation history. If we detect that the chatCtx has been updated to include these messages, we can send them to Phonic using the add_system_message message. This will allow the user to steer the conversation without calling generateReply

Changes Made

• Change updateChatCtx to add an appendum to the system_message if the chat context is not empty on initialization.
• Use llm.computeChatCtxDiff to check if there are new items in the Chat context, and call sendAddSystemMessage if a system or developer message

Video Demo

https://drive.google.com/file/d/12-6KNPaw830kCm1wm9xv3CShOycsPDAm/view?usp=sharing

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: A small video demo showing changes works as expected and did not break any existing functionality using Agent Playground (if applicable)

Testing

• Automated tests added/updated (if applicable)
• All tests pass
• Make sure both restaurant_agent.ts and realtime_agent.ts work properly (for major changes)

Additional Notes

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Note to reviewers: Please ensure the pre-review checklist is completed before starting your review.

[changeset-bot]

🦋 Changeset detected

Latest commit: c8efe5c

The changes in this PR will be included in the next version bump.

This PR includes changesets to release 21 packages

Name	Type
@livekit/agents-plugin-phonic	Patch
@livekit/agents	Patch
@livekit/agents-plugin-anam	Patch
@livekit/agents-plugin-baseten	Patch
@livekit/agents-plugin-bey	Patch
@livekit/agents-plugin-cartesia	Patch
@livekit/agents-plugin-deepgram	Patch
@livekit/agents-plugin-elevenlabs	Patch
@livekit/agents-plugin-google	Patch
@livekit/agents-plugin-hedra	Patch
@livekit/agents-plugin-inworld	Patch
@livekit/agents-plugin-lemonslice	Patch
@livekit/agents-plugin-livekit	Patch
@livekit/agents-plugin-neuphonic	Patch
@livekit/agents-plugin-openai	Patch
@livekit/agents-plugin-resemble	Patch
@livekit/agents-plugin-rime	Patch
@livekit/agents-plugin-sarvam	Patch
@livekit/agents-plugin-silero	Patch
@livekit/agents-plugin-xai	Patch
@livekit/agents-plugins-test	Patch

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