Add the shortcode option to dynamic tags for background images in Elementor

shortcode_image_tag.php

<?php
// place the snippet inside the functions.php file from your WordPress child theme

use Elementor\Controls_Manager;
add_action( 'elementor/dynamic_tags/register_tags', function( $dynamic_tags ) {
	class Custom_Image_Tag extends Elementor\Core\DynamicTags\Data_Tag {

		public function get_name() {
			return 'shortcode-image';
		}

		public function get_categories() {
			return [ 'image' ];
		}

		public function get_group() {
			return [ 'site' ];
		}

		public function get_title() {
			return 'Shortcode Image';
		}

		protected function _register_controls() {
			$this->add_control(
				'shortcode',
				[
					'label' => __( 'Shortcode', 'elementor-pro' ),
					'type'  => Controls_Manager::TEXTAREA,
				]
			);
		}

		protected function get_value( array $options = [] ) {
			$settings = $this->get_settings();

			if ( empty( $settings['shortcode'] ) ) {
				return;
			}
			
			return [
				'url' => do_shortcode( $settings['shortcode'] ) // Your shortcode MUST return a full valid URL
			];
		}
	}
	$dynamic_tags->register_tag( 'Custom_Image_Tag' );
});

This code adds the missing option