webui: clarify API connection badge

tests/test_http_api_contract.py

@@ -366,3 +366,12 @@ def test_embedded_webui_config_subtabs():
     assert "config-maintenance" in source
     assert "WiFi / AP" in source
     assert "Maintenance" in source
+
+
+def test_embedded_webui_api_badge_labels_are_clear():
+    source = firmware_source()
+
+    assert "API Connecting..." in source
+    assert "API Live" in source
+    assert "API Error" in source
+    assert 'textContent="Offline"' not in source