Product categories widget is not the filter widget. This is the default WooComerce widget that displays a list of categories but does not filter by the categories.
To filter by categories you need to look for filter plugins. There are a lot of free https://wordpress.org/plugins/search/filters/ and paid filter plugins but we did not study them very carefully to check which one has the categories filter you need. Check the description of the plugins to get more information about this.
