feat: Home Assistant integration — WebSocket connection, automation conditions, UI

Add full Home Assistant integration via WebSocket API:
- HARuntime: persistent WebSocket client with auth, auto-reconnect, entity state cache
- HAManager: ref-counted runtime pool (like WeatherManager)
- HomeAssistantCondition: new automation trigger type matching entity states
- REST API: CRUD for HA sources + /test, /entities, /status endpoints
- /api/v1/system/integrations-status: combined MQTT + HA dashboard indicators
- Frontend: HA Sources tab in Streams, condition type in automation editor
- Modal editor with host, token, SSL, entity filters
- websockets>=13.0 dependency added

server/src/wled_controller/api/routes/system.py

@@ -21,6 +21,8 @@ from wled_controller.api.dependencies import (
     get_automation_store,
     get_color_strip_store,
     get_device_store,
+    get_ha_manager,
+    get_ha_store,
     get_output_target_store,
     get_pattern_template_store,
     get_picture_source_store,
@@ -311,3 +313,52 @@ def list_api_keys(_: AuthRequired):
         for label, key in config.auth.api_keys.items()
     ]
     return {"keys": keys, "count": len(keys)}
+
+
+@router.get("/api/v1/system/integrations-status", tags=["System"])
+async def get_integrations_status(
+    _: AuthRequired,
+    ha_store=Depends(get_ha_store),
+    ha_manager=Depends(get_ha_manager),
+):
+    """Return connection status for external integrations (MQTT, Home Assistant).
+
+    Used by the dashboard to show connectivity indicators.
+    """
+    from wled_controller.core.devices.mqtt_client import get_mqtt_service
+
+    # MQTT status
+    mqtt_service = get_mqtt_service()
+    mqtt_config = get_config().mqtt
+    mqtt_status = {
+        "enabled": mqtt_config.enabled,
+        "connected": mqtt_service.is_connected if mqtt_service else False,
+        "broker": (
+            f"{mqtt_config.broker_host}:{mqtt_config.broker_port}" if mqtt_config.enabled else None
+        ),
+    }
+
+    # Home Assistant status
+    ha_sources = ha_store.get_all_sources()
+    ha_connections = ha_manager.get_connection_status()
+    ha_status_map = {s["source_id"]: s for s in ha_connections}
+    ha_items = []
+    for source in ha_sources:
+        status = ha_status_map.get(source.id)
+        ha_items.append(
+            {
+                "source_id": source.id,
+                "name": source.name,
+                "connected": status["connected"] if status else False,
+                "entity_count": status["entity_count"] if status else 0,
+            }
+        )
+
+    return {
+        "mqtt": mqtt_status,
+        "home_assistant": {
+            "sources": ha_items,
+            "total": len(ha_sources),
+            "connected": sum(1 for s in ha_items if s["connected"]),
+        },
+    }