I've run into this same problem with Godot 4.4.1 and Firefox. First of all, I see the same error when using these test instructions from Godot's docs, so the problem isn't only with itch.
Second of all, I find that if I edit my game page to turn SharedArrayBuffer support on, the game launches now. In my limited testing, if I export the Godot project with thread support on, it worked on itch once and afterwards starting giving Array Index Out of Bounds again. It seems to work consistently when exported with thread support off.
SharedArrayBuffer support on itch is considered an experimental feature, and it's still being changed (for example, currently the game launches in a new window, and there is no way for the developer to set the window size or remove the fullscreen button). But at least the game loads.
P.S. The option for single-threaded web export was added in Godot 4.3. It's supposed to work without SharedArrayBuffer support on, but in this case, that seems to not be working. The problem isn't widely reported though, so idk what the deal is.
P.P.S. the linked Godot instructions say to run python serve.py --root , but I found I had to run python serve.py -r ./