tried your game but the mouse thing is killing me.
in web builds the browser drops the pointer lock on its own (Esc, a tab switch, a click outside the itch frame) and only grants it again during a real click.
i fixed this by checking Input.mouse_mode every frame, pause when it's no longer MOUSE_MODE_CAPTURED, and set Input.mouse_mode = Input.MOUSE_MODE_CAPTURED only inside a click handler (the RESUME button, or a left-click in _unhandled_input), never from _ready or _process
hope this helps