ninja_forms_upgrade_action_{action_name}.php

<?php

add_filter( 'ninja_forms_upgrade_action_my_addon', 'upgrade_my_addon_settings' );

function upgrade_my_addon_settings( $action_settings ){
  
  $old_setting = $action_setting[ 'old_setting' ];
  
  // Modify $old_setting
  
  $action_settings[ 'new_setting' ] = $old_setting;
  
  return $action_settings;
}