Use live MQTT readiness for server health checks

internal/web/server_test.go

@@ -162,3 +162,19 @@ func TestReportedScenariosDoNotClaimHardwareCompatibility(t *testing.T) {
 		t.Fatal("scenario aliases retained history")
 	}
 }
+
+func TestHealthUsesCurrentMQTTReadiness(t *testing.T) {
+	v := testViewer()
+	ready := false
+	v.SetReadiness(func() bool { return ready })
+	for _, want := range []int{503, 200, 503} {
+		ready = want == 200
+		// No connection event retained: current readiness must still work.
+		r := httptest.NewRequest("GET", "http://127.0.0.1:8080/healthz", nil)
+		w := httptest.NewRecorder()
+		v.Handler().ServeHTTP(w, r)
+		if w.Code != want {
+			t.Fatalf("health status %d, want %d", w.Code, want)
+		}
+	}
+}