Hi,
The main issue is, that the whole setup is used on a taxonomy archive page, that will not work unfortunately. The tutorial only works on a single page, with the WooCommerce products (not Products archive) widget.
If you move this to a single page, it should start working immediately.
PHP code is not allowed in those fields – and for the Elementor Widget output it would not make any difference either, as it is generated by Elementor. Those fields only work if you use the default live search container of the plugin.
If you want to use PHP, I recommend using the asp_results hook instead.