Allow products and terms from multiple taxonomies to share rewrite base /product for rule

share-rewrite-base.php

<?php

// option 1
add_action('parse_request', function () {
    
    global $wp_rewrite, $wp, $wp_query;
    
    if (isset($wp->query_vars['product'], $wp->query_vars['post_type']) && $wp->query_vars['post_type'] === 'product') {
        
        $matched   = false;
        $term_name = $wp->query_vars['product'];
        
        $taxonomy_1 = 'product_type';
        $taxonomy_2 = 'product_size';
        
        if (($exists = term_exists($term_name, $taxonomy_1)) && isset($exists['term_id'])) {
            $matched = true;
            $taxonomy = $taxonomy_1;
        } elseif (($exists = term_exists($term_name, $taxonomy_2)) && isset($exists['term_id'])) {
            $matched = true;
            $taxonomy = $taxonomy_2;
        }
        
        if ($matched) {
            $wp->query_vars = array(
                $taxonomy => $term_name,
            );
        }
    }
});

// option 2
add_action('pre_get_posts', function ($query) {
    
    if ($query->is_main_query()) {
        
        if (get_query_var('post_type') === 'product' && ($term_name = get_query_var('product'))) {
            
            $matched    = false;
            $taxonomy_1 = 'product_type';
            $taxonomy_2 = 'product_size';
            
            if (($exists = term_exists($term_name, $taxonomy_1)) && isset($exists['term_id'])) {
                $matched  = true;
                $taxonomy = $taxonomy_1;
            } elseif (($exists = term_exists($term_name, $taxonomy_2)) && isset($exists['term_id'])) {
                $matched  = true;
                $taxonomy = $taxonomy_2;
            }
            
            if ($matched) {
                $query->query = array($taxonomy => $term_name);
                
                unset($query->query_vars['page']);
                unset($query->query_vars['product']);
                unset($query->query_vars['post_type']);
                
                // reset all flags
                $query->init_query_flags();
                $query->is_tax     = true;
                $query->is_archive = true;
                
                $query->set('name', '');
                $query->set($taxonomy, $term_name);
                
                // we need to call parse_tax_query again to have the tax_query property
                // on WP_Query class populated based on the query vars set above
                /** @var \WP_Query  $query */
                $query->parse_tax_query($query->query_vars);
            }
        }
    }
});