We noticed that when we have a web map that contains a route layer, each individual layer within the route layer (Stops, DirectionPoints, DirectionLines, RouteInfo) gets represented as a single layer within the Layer List of a Map widget within Experience Builder.
This causes individual layer visibility toggles configured and saved within the web map to be ignored in Experience Builder, and you also don't have the ability to toggle on or off the individual Route Layer layers since they are represented as a single layer in the Map widget's Layer List.
For comparison sake, when you add a map service to the web map that has multiple individual layers within the single service, it correctly honors individual layer visibility and shows each individual layer within the Map widget's Layer List (allowing you to toggle them on and off independently).
Please see attached image. The route layer is shown as a single layer (but really has four individual layers within it), whereas the map service correctly shows all individual layers contained within the service.