An example function showing how to convert a WordPress category id to a slug.

widget.php

<?php

function prefix_convert_category_id_to_slug( $value ) {

    if ( is_int( $value ) ) {
        $category = get_term( $value, 'category' );
        if ( is_wp_error( $category ) ) {
            return $value;
        }
        $value = $category->slug;
    }
    
    return $value;
    
}