For now, my best guess is that the Menu is sitting on top of the whole page on load. Even though it is at 0 opacity it is still covering and nothing below it can be hovered/selected. Think of it like a piece of glass. You can see through it, but it is still a solid barrier.
The close menu interaction, must be turning the menu to display:none as well as dropping the opacity. Add an initial state of display:none to the menu. I think that should solve it.
Like I mentioned above, if you share the project read-only link, then we can confirm if that is in fact the issue or note. Hope that helps and welcome to the community!