Set up an interaction on all your navlinks, make it a “mouse click”. You may then just use your “hidedesktopmenu” interaction I guess. When clicked the page will scroll and nav overlay will disappear. Just check your interactions closely - they have missing components. Perhaps they were the menu cross at the top right which should also disappear in this sequence.
I made the adjustment in the interaction to hide the close button, just like you said. But after the click, the menu hamburger does not appear, I can not understand the reason, because the hide event is related to the close button - not related with hamburger menu.
do not add anything in regards to burger icon to the hide desktop interaction.
Instead add anotheron click interaction to the menu buttons, that is called BurgerIconAnimation-Out. This is the one that makes a burger appear.
We need to add another interaction because appearance of the burger icon is very complex, so integrating it would be tedious. So we are using already present interaction!