fix(agents): prevent crash when child process dies

[Hormold]

Description

Fix supervisor process crashes when child process dies unexpectedly

Changes Made

• Wrap pidusage() in try-catch, return 0 if process is gone (ENOENT)
• Check proc.connected before all send() calls to avoid ERR_IPC_CHANNEL_CLOSED
• Call clearTimers() in exit handler (was only in error handler)
• Remove throw err after reject(err) in setTimeout (was causing uncaught exception) (not sure here)

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

Testing

• Automated tests added/updated (if applicable)
• All tests pass

---

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

[changeset-bot]

🦋 Changeset detected

Latest commit: 59c7d1a

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

This PR includes changesets to release 16 packages

Name	Type
@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-inworld	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-silero	Patch
@livekit/agents-plugins-test	Patch

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