Think, widget input and game input as different state. It cannot be called at once.
Whenever your focus is outside the widget, then it will call use the binding that you specified in Game Input (whether in Player Controller or PlayerCharacter). And when your focus is on the widget, you can execute all the key bindings that specified in that particular widget.
Or you can create a function that always return the Focus into the Widget, whenever a key is pressed. Or, you can duplicate all the game key-binding into the widget.