How to display Elementor widget from another Elementor widget using PHP

I create a custom Elementor widget like plugin and want to use another Elementor widget from it. It is not a problem to show a standard WordPress widget (code in the function render()):

the_widget('WP_Widget_Calendar');

It is not a problem to show a post with Elementor widgets:

$plugin = ElementorPlugin::instance();
echo $plugin->frontend->get_builder_content_for_display($any_post_id);

Also I see with this code

global $wp_widget_factory;
echo '<pre>'; var_dump($wp_widget_factory->widgets); echo '</pre>';

all registered widgets:

"WP_Widget_Pages"                                          
"WP_Widget_Calendar"                                       
"WP_Widget_Archives"                                       
"WP_Widget_Media_Audio"                                    
"WP_Widget_Media_Image"                                    
"WP_Widget_Media_Gallery"                                  
"WP_Widget_Media_Video"                                    
"WP_Widget_Meta"                                           
"WP_Widget_Search"                                         
"WP_Widget_Text"                                           
"WP_Widget_Categories"                                     
"WP_Widget_Recent_Posts"                                   
"WP_Widget_Recent_Comments"                                
"WP_Widget_RSS"                                            
"WP_Widget_Tag_Cloud"                                      
"WP_Nav_Menu_Widget"                                       
"WP_Widget_Custom_HTML"                                    
"MSP_Main_Widget"                                          
"RevSliderWidget"                                          
"WpfWoofiltersWidget"                                      
"wp_ulike_widget"                                          
"WC_Widget_Cart"                                           
"WC_Widget_Layered_Nav_Filters"                            
"WC_Widget_Product_Categories"                             
"WC_Widget_Product_Search"                                 
"WC_Widget_Product_Tag_Cloud"                              
"WC_Widget_Products"                                       
"WC_Widget_Recently_Viewed"                                
"WC_Widget_Top_Rated_Products"                             
"WC_Widget_Rating_Filter"                                  
"MC4WP_Form_Widget"                                        
"Element_Pack_Elementor_Template_Widget"                   
"aux_about_widget"                                         
"aux_recent_post_widget"                                   
"aux_popular_posts_widget"                                 
"aux_testimonial"                                          
"aux_staff"                                                
"aux_audio"                                                
"aux_code"                                                 
"aux_contact_form"                                         
"aux_divider"                                              
"aux_gmaps"                                                
"aux_image"                                                
"aux_before_after"                                         
"aux_accordion_widget"                                     
"aux_tabs_widget"                                          
"aux_recent_product"                                       
"aux_latest_posts_slider"                                  
"aux_quote"                                                
"aux_search"                                               
"aux_socials_list"                                         
"aux_video"                                                
"aux_contact_box"                                          
"aux_advance_recent_product"                               
"aux_latest_vendors"                                       
"ElementorProModulesLibraryWP_WidgetsElementor_Library"
"AUXSHP_WC_Widget_Price_Filter"                            
"AUXSHP_WC_Widget_Recent_Reviews"                          
"AUXSHP_WC_Widget_Layered_Nav"                             

But how to show another data driven Elementor widget from the PHP-code in render()?

My attempt to do this with this code did not work:

$data = self::build_data(...);
$element = new ElementorProModulesCarouselWidgetsMedia_Carousel($data);
$element->print_element();

Thank you for your guidance.