agroexpert/partials/category-menu.php

<?php

// Получаем текущие рубрики из меню
$categories = get_categories_from_menu_exact_order('rubrics');

foreach ($categories as $category) {
    if ($category->slug === 'uncategorized') continue;

    $icon = get_field('icon', 'category_' . $category->term_id);
    $bg_image = get_field('bg_image', 'category_' . $category->term_id);
    $category_link = get_category_link($category->term_id);
?>
<?php if ($icon) : ?>
    <a href="<?php echo esc_url($category_link); ?>" class="menu-link">
        <div class="menu-link__bg">
            <?php if ($bg_image) : ?>
                <img src="<?php echo esc_url($bg_image['url']); ?>" alt="<?php echo esc_attr($category->name); ?>" />
            <?php endif; ?>
        </div>
        <div class="menu-link__icon">
            <?php if ($icon) : ?>
                <img src="<?php echo esc_url($icon); ?>" alt="<?php echo esc_attr($category->name); ?>" />
            <?php endif; ?>
        </div>
        <span class="menu-link__text"><?php echo esc_html($category->name); ?></span>
    </a>
<?php endif; ?>    
<?php
}
?>