Summary

Webchat and other WebSocket clients can't display thinking/reasoning content during streaming - it only appears after the turn completes when history is reloaded.

Current Behavior

1. Agent has extended thinking enabled (e.g., thinkingLevel: "low")
2. During streaming, assistant events only contain text/delta - no thinking
3. Thinking content is only available via chat.history after the turn completes
4. Clients have to reload history post-completion to show thinking blocks

Expected Behavior

Thinking content should be emitted as agent events during streaming, allowing clients to display it in real-time (like claude.ai does).

Proposed Solution

In src/agents/pi-embedded-subscribe.ts, the emitReasoningStream function currently only calls params.onReasoningStream. It should also emit an agent event:

const emitReasoningStream = (text: string) => {
  if (!state.streamReasoning || !params.onReasoningStream) return;
  const formatted = formatReasoningMessage(text);
  if (!formatted) return;
  if (formatted === state.lastStreamedReasoning) return;
  state.lastStreamedReasoning = formatted;
  
  // ADD: Emit as agent event for webchat/WS clients
  emitAgentEvent({
    runId: params.runId,
    stream: "thinking",  // or include in "assistant" with data.thinking
    data: { thinking: formatted },
  });
  
  void params.onReasoningStream({ text: formatted });
};