Edit snippet to use rank math primary category for if there is no primary?

Hello,

I found the following snippet in another post here to use the Rank Math primary category to show the primary category instead of all categories on some query loop blocks I set up:

/*add primary category for buttons for posts*/
add_filter('render_block', function ($block_content, $block) {
    if (
        !is_admin() &&
        !empty($block['attrs']['className']) &&
        strpos($block['attrs']['className'], 'placeholder-for-primary-cat') !== false
    ) {
        $cat = false;
        $primary_cat_id = get_post_meta( get_the_ID(), 'rank_math_primary_category', true );

        if ($primary_cat_id) {
            $cat = get_term($primary_cat_id, 'category');
            if (!is_wp_error($cat)) {
                $primary_cat = $cat->name;
                $primary_term_url = get_term_link($cat);
                $primary_term_output = '<a class="primary-cat-' . esc_attr($primary_cat) . '" href="' . esc_url($primary_term_url) . '">' . esc_html($primary_cat) . '</a>';
                $block_content = str_replace('primary-category-placeholder', $primary_term_output, $block_content);
            }
        } else {
            $categories = get_the_category();
            $first_category = '';

            if (!empty($categories)) {
                $first_category = $categories[0]->name;
                $first_category_url = get_term_link($categories[0]);
                $first_category_output = '<a class="primary-cat-' . esc_attr($first_category) . '" href="' . esc_url($first_category_url) . '">' . esc_html($first_category) . '</a>';
                $block_content = str_replace('primary-category-placeholder', $first_category_output, $block_content);
            }
        }
    }
    return $block_content;
}, 10, 2);

…it looked great. However, I found that, as I had implemented Rank Math recently, some older posts did not have a primary category yet and these posts all had a critical error until I removed the snippet.

Is there any way to edit this so that it will show either nothing or one category and not a critical error until I can get around to adding a primary category to all posts?

Thanks