- Default sid to self.client_id when not explicitly provided, matching
every other WS message dispatch (executing, executed, progress_state, etc.)
- Previously sid=None caused broadcast to all connected clients
- Format signature per ruff, remove redundant comments
- Add unit tests for routing, legacy format, and new prompt_id format
Amp-Thread-ID: https://ampcode.com/threads/T-019ca3ce-c530-75dd-8d68-349e745a022e