Are there any scripts, classes, and/or functions built-in to WP for a plugin to export/import its saved data from wp_options?

The only native import/export facility is the one under Tools in the admin. And even that needs an extension (plugin) for importing from different formats.

It’s pretty straightforward to build one yourself. Something along the lines of:

$options = get_my_options();
header( 'Content-disposition: attachment; filename=my_export.txt' );
header( 'Content-Type: text/plain' );
echo json_encode( $options );
exit;

And conversely:

if ( ! empty( $_FILES['my_import']['tmp_name'] ) ) {
   if ( $import = file_get_contents( $_FILES['my_import']['tmp_name'] ) ) {
       if ( $options =@ json_decode( $import ) ) {
           save_my_options( $options );
       }
   }
}