fix: wait for agent before sending text

agent/agent.py

@@ -758,6 +758,17 @@ async def handle_job(ctx: JobContext) -> None:
     )
 
     await ctx.connect()
+    # The participant can appear in the browser slightly before AgentSession is
+    # ready to accept lk.chat streams. Explicitly signal readiness so the first
+    # typed message is never raced against session startup.
+    try:
+        await ctx.room.local_participant.publish_data(
+            json.dumps({"type": "agent_ready"}),
+            reliable=True,
+            topic="conversation-control",
+        )
+    except Exception as exc:  # noqa: BLE001
+        logger.warning("failed to publish agent readiness: %s", exc)
     logger.info("Agent connected to room %s", ctx.room.name)