Fix stale OpenAI Responses WebSocket reuse

[MMYurt]

Summary

• add an optional validate_cb to ConnectionPool so unavailable pooled connections can be discarded before reuse
• configure the OpenAI Responses WebSocket pool to reject connections whose closed state is already known
• add hermetic regression coverage for both the generic pool and the OpenAI Responses transport

Fixes #6513.

Problem

Concurrent Responses API requests can grow the WebSocket pool to multiple connections. If one or more of those connections close while idle, a later request may reuse a known-closed socket and fail at send_str(). The outer LLM retry eventually recovers, but each stale connection can add a warning and retry backoff to a live voice turn.

This change removes connections that fail a cheap, synchronous validation before returning them from the pool. The OpenAI transport uses not ws.closed for that check. Existing retry behavior remains unchanged for races where a connection becomes unusable after validation or during the send itself.

Testing

• uv run pytest tests/test_connection_pool.py --unit -q (5 passed)
• uv run pytest tests/test_plugin_openai_responses.py --plugin openai -q (3 passed)
• make check (format, lint, and strict mypy across 623 source files)

Additional local unit-suite validation completed 1,216 tests with 4 skipped. Nine tests/test_room.py cases could not set up because the local machine does not have the external livekit-server binary installed.

[CLAassistant]

All committers have signed the CLA.

[devin-ai-integration]

✅ Devin Review: No Issues Found

Devin Review analyzed this PR and found no bugs or issues to report.