Hello,
Dynamic elements like filters can work on the WooCommerce shop page only. If you create a custom page and do not set it as the shop page, filters and categories will lead to the defined shop page.
In your case, the custom elements like the search bar, banner categories, and sidebar filters are not working dynamically because they need to be used on the designated WooCommerce shop page for the AJAX functionality to work as expected.
To achieve the dynamic behavior you described, you should set the default WooCommerce shop page in your settings and then customize it with the elements you need. This way, when a user selects a category or applies filters, the results will be displayed directly on the same page without redirection, and you can utilize AJAX functionality.
If you need further assistance with this setup or have any other questions, please let us know.
Best regards