Run the steering safety cases through ThreadManagementService so they cover
the delivery result returned to MCP callers and subsequent queued-turn delivery.

Keep the upstream task-ownership regression on an explicitly safe native-steering
fixture, preserving its assertions while Claude agent messages use the queue.

Co-Authored-By: GPT-6.1 Sol at high effort <noreply@openai.com>
Co-Authored-By: GPT-6.1 Sol at xhigh effort, review subagents <noreply@openai.com>