From one Godot dev to another: make sure to enable "SharedArrayBuffer support" from the "edit game" menu on itch. It should be under Embed options -> Frame options. This will make the game playable in browser!
I don't know the deal with "Cross-Origin Isolation", but I ran across the former issue when I was putting my first game up on itch. In the meantime, I'll be playing and rating the Windows version instead :)