fix: restore real-time chat responses via WebSocket (#98)

The chat WebSocket return path was broken by two bugs that prevented
Timmy's responses from appearing in the live chat feed:

1. Frontend checked msg.type instead of msg.event for 'timmy_response'
   events — the WSEvent dataclass uses 'event' as the field name.
2. Frontend accessed msg.response instead of msg.data.response — the
   response payload is nested in the data field.

Additional fixes:
- Queue acknowledgment ("Message queued...") no longer logged as an
  agent message in chat history; the real response is logged by the
  task processor when it completes, eliminating duplicate messages.
- Chat message template now carries data-task-id so the WS handler
  can find and replace the placeholder with the actual response.
- appendMessage() uses DOM APIs (textContent) instead of innerHTML
  for safer content insertion before markdown rendering.
- Fixed chat_message.html script targeting when queue-status div is
  present between the agent message and the inline script.

https://claude.ai/code/session_011cJfexqBBuGhSRQU8qwKcR

Co-authored-by: Claude <noreply@anthropic.com>

src/dashboard/app.py

@@ -176,6 +176,15 @@ async def _task_processor_loop() -> None:
             context = f"[System: Current date/time is {now.strftime('%A, %B %d, %Y at %I:%M %p')}]\n\n"
             response = timmy_chat(context + task.description)
 
+            # Log the real agent response to chat history
+            try:
+                from dashboard.store import message_log
+                timestamp = now.strftime("%H:%M:%S")
+                message_log.append(role="agent", content=response, timestamp=timestamp)
+            except Exception as e:
+                logger.debug("Failed to log response to message_log: %s", e)
+
+            # Push response to chat UI via WebSocket
             try:
                 from infrastructure.ws_manager.handler import ws_manager
                 asyncio.create_task(