Query categories that have a description

How about looping all available terms, if term has description, add to to an object_ids, something like this.

add_filter(
    'wp_sitemaps_taxonomies_query_args',
    function( $args, $taxonomy ) {
        // Show in sitemap categories and topics that have a description
        if ( $taxonomy == 'category' || $taxonomy == 'post_tag' ) {
            // get the terms of the taxonomy
            $terms = get_terms( 'post_tag', [
                'hide_empty' => false, // change to true if you want not empty terms
                'taxonomy'   => $taxonomy,
            ]);

            // will contain all ids of terms that have description
            $object_ids = [];

            // loop terms
            foreach ($terms as $term) {
                // if term has description, add its id to our array
                if (!empty($term->description)) $object_ids[] = $term->term_id;
            }

            // if we have ids (found terms with description) add it to the filter $args
            if (!empty($object_ids)) $args['object_ids'] = $object_ids;
        }

        return $args;
    },
    10,
    2
);