fix(inference): prefer inference credentials for interruption detector

[GaureeshAnvekar]

Description

Fixes adaptive interruption detector credential precedence when using a self-hosted LiveKit SFU with LiveKit Cloud Inference. Issue #1353

Previously, adaptive interruption could pick up LIVEKIT_API_KEY / LIVEKIT_API_SECRET before LIVEKIT_INFERENCE_API_KEY / LIVEKIT_INFERENCE_API_SECRET as described in the issue, causing Cloud inference websocket auth to fail with 401 when the SFU credentials were local/self-hosted credentials.

Changes Made

• Prefer inference-specific env vars for adaptive interruption auth.
• Preserve fallback to regular LiveKit credentials when inference-specific credentials are not set.

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

• All tests pass

Additional Notes

Before change (local SFU):

After change (local SFU):

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