This sample demonstrates how to add a Legend component instance to a LayerList component. This is achieved by adding the legend string to the panel of the appropriate ListItem in the LayerList component.
      document.querySelector("arcgis-layer-list").listItemCreatedFunction = (event) => {
        const { item } = event;
        // Exclude group layers, otherwise the legend will be displayed twice
        if (item.layer.type != "group") {
          item.panel = {
            content: "legend",
            open: true,
          };
        }
      };