Select the base
Control node of your overlayed control, say
Control or whatever it is. Set its Mouse -> Filter parameter to "Stop", so input will stop propagating when it reachs its layer. Or you can just set each button to stop if there are no tangible/palpable parent container.
It's a magic parameter, "ignore" will ignore all inputs, "pass" will get the input event but keeps propagating, "stop" will get the input event and set it as handled stoping its propagation.
Children of control can have different mouse filters, for example, a big
Container holding a small
Button has stop filter, but the button has pass, so you can click the button but it prevents clicking whatever is under the container.