It is not that difficult, first add a ir.filters object or an ir.actions.server . This contains the real filter.  (I'm using an existing example here)

The currently existing filters are stored in the website_sale module in the data folder.

id="dynamic_snippet_newest_products_filter" model="ir.filters">
    name="name">Newest Products
    name="model_id">product.product
    name="user_id" eval="False" />
    name="domain">[('website_published', '=', True)]
    name="context">{'display_default_code': False, 'add2cart_rerender': False}
    name="sort">['create_date desc']
    name="action_id" ref="website.action_website"/>

If necessary you can add python code eg:

        
id="dynamic_snippet_latest_sold_products_action" model="ir.actions.server">
            name="name">Recently Sold Products
            name="model_id" ref="model_product_product"/>
            name="state">code
            name="code">
DynamicFilter = model.env['website.snippet.filter']
response = DynamicFilter._get_products('latest_sold', model.env.context)
                    
                  

Then add a website.snippet.filter eg:

id="dynamic_filter_newest_products" model="website.snippet.filter">
    name="filter_id" ref="website_sale.dynamic_snippet_newest_products_filter"/>
    name="field_names">display_name,description_sale,image_512,price:monetary
    name="limit" eval="16"/>
    name="name">Newest Products
or with an action:
id="dynamic_filter_latest_sold_products" model="website.snippet.filter">
    name="action_server_id" ref="website_sale.dynamic_snippet_latest_sold_products_action"/>
    name="field_names">display_name,description_sale,image_512,price:monetary
    name="limit" eval="16"/>
    name="name">Recently Sold Products

Voila, you have your new filters available on the website product carousel :-)