feat: session busy indicator — daemon tracks mid-turn state (agent_start/settled), busy field on session rows + live broadcast; pulsing pip in sidebar and cards (265 web tests, daemon 95.4%)

daemon/hub_extra_test.go

@@ -714,3 +714,34 @@ func TestWebResubscribeSplitsEventBatches(t *testing.T) {
 	_ = agent2.WriteJSON(map[string]any{"v": 1, "type": evMessageUpdate, "sessionId": "s2", "seq": 1, "ts": 11, "delta": "two"})
 	readBatch("s2") // event B must arrive as its own frame, never mixed with A's
 }
+
+func TestHubBusyFlagLifecycle(t *testing.T) {
+	ts, _, hub := newTestServerHub(t)
+	ws := dialAgent(t, ts)
+	defer ws.Close()
+	_ = ws.WriteJSON(helloFrame("busy-1"))
+	_ = readFrame(t, ws)
+	sendEv := func(typ string, seq int64) {
+		_ = ws.WriteJSON(map[string]any{
+			"v": 1, "sessionId": "busy-1", "seq": seq, "ts": 1, "type": typ,
+		})
+	}
+	sendEv("agent_start", 1)
+	waitFor(t, 3*time.Second, func() bool {
+		for _, s := range hub.SessionsView() {
+			if s.ID == "busy-1" {
+				return s.Busy
+			}
+		}
+		return false
+	})
+	sendEv("agent_settled", 2)
+	waitFor(t, 3*time.Second, func() bool {
+		for _, s := range hub.SessionsView() {
+			if s.ID == "busy-1" {
+				return !s.Busy
+			}
+		}
+		return false
+	})
+}