enqueue admin styling and scripts only on plugin page

You can use $screen = get_current_screen(); functions to get the current screen and add warp your enqueue method with the if conditions to check the screen.

https://codex.wordpress.org/Function_Reference/get_current_screen

public function enqueue_scripts() {

$screen = get_current_screen();

  // Check screen base and page
  if ( 'options-general' === $screen->base && $_GET['page'] ==='uwc' )
 {
    wp_enqueue_script( $this->plugin_name, plugin_dir_url( __FILE__ ) . 'js/wp-color-picker-script.js', array( 'wp-color-picker' ), false, true );

 } 
}