[WP][WC] Remove / Hide WooCommerce product tags, the right way

woo_remove_product_tags.php

<?php

// Overwrite product_tag taxonomy properties
add_action('init', function() {
    register_taxonomy('product_tag', 'product', [
        //'public'            => false, // making it not public could throw errors in some themes / plugins
        'show_ui'           => false,
        'show_admin_column' => false,
        'show_in_nav_menus' => false,
        'show_tagcloud'     => false,
    ]);
}, 100);

// Remove the column from Products list
add_action( 'admin_init' , function() {
    add_filter('manage_product_posts_columns', function($columns) {
        unset($columns['product_tag']);
        return $columns;
    }, 100);
});

?>