WooCommerce custom taxonomy page filter

Question

I am editing the taxonomy template, say taxonomy-brand.php, but within this page I'd like to add a set of clickable categories to filter the list of products.

So, if I have a brand of Adidas for example, I'd like the taxonomy list to show all Adidas products but also have clickable filters to limit the list to Football, Athletics etc

I know I can get the terms for the taxonomy via

$terms = get_terms([
    'taxonomy' => $taxonomy,
    'hide_empty' => false,
]);
foreach ($terms as $term){
    ...
}   

I'm just not sure of the way to reload the page with the category filter in place.

Answer 1

Seems this is another simple functionality that requires massive hacking of WordPress functions. Writing long-winded, inefficient process to get around the limitations