I know little of these things, but itch requires the index.html and nothing else. It does not "know" what kind of game you have, it just fires up the index.html insided the embed on your project page, as far as I know. Your game boot logic must start inside the index.html and somehow start your game up. Very likely inside the index.js that will be referenced within the index.html.
You have to have some kind of initialisation and declare ressources and whatnot. The scripts I found when checking, if Godot can split the pck did some things where they loaded each of the pck in some sort of initi phase. Maybe your web export has to be ajusted for that.