copy fields value to another field

by

You do not need to, instead add the user URL column to the list of searchable table columns

https://developer.wordpress.org/reference/hooks/user_search_columns/

Which includes a user contributed example that does this:

https://developer.wordpress.org/reference/hooks/user_search_columns/#comment-4605

add_filter( 'user_search_columns', 'wpdocs_filter_function_name', 10, 3 );
     
function wpdocs_filter_function_name( $search_columns, $search, $wp_user_query ) {
    $search_columns[] = 'user_url';
    return $search_columns;
}

With this, no syncing to a URL field is necessary.