fix(provider): reuse falsy websocket models

[hsusul]

Summary

OpenAIProvider uses truthiness to detect a cached websocket model. A valid Model instance with falsey truthiness is therefore recreated on every lookup in the same running loop. Check cache-key presence instead so all cached model instances are reused.

Test plan

• Added regression coverage for a falsey websocket model and identity reuse.
• Focused: 2 passed (tests/test_config.py -k falsy_websocket_model or scopes_websocket_model_cache).
• Full verification: UV_CACHE_DIR=/tmp/uv-verify-pr5-b2 UV_DEFAULT_INDEX=https://pypi.org/simple bash .agents/skills/code-change-verification/scripts/run.sh — all commands passed (format, lint, typecheck, tests).

Issue number

N/A

Checks

• I've added new tests, if relevant
• I've run .agents/skills/code-change-verification/scripts/run.sh
• I've confirmed all verification steps pass
• If using Codex, I've run /review before submitting this PR