fix: keep LiveKit rooms alive so agent survives reconnects

Set room.empty_timeout to 86400 (24h) in livekit.yaml. Previously the
default 300s timeout destroyed the room when all participants left,
which killed the agent job and left no worker registered for the next
join — causing 'assistant not ready retry' on tab reopen.

livekit.yaml

@@ -6,3 +6,10 @@ rtc:
 
 keys:
   devkey: devsecret
+
+# Keep rooms alive for 24h — the agent stays resident so reconnections
+# don't require a fresh dispatch. Without this, LiveKit destroys the room
+# after empty_timeout (default 300s), kills the agent job, and the next
+# join finds no worker registered ("assistant not ready retry").
+room:
+  empty_timeout: 86400