We can render a media control for print the image URL in a custom <img> tag. For the same we can use  wp_get_attachment_image() function to generate the image markup. The following code is example of rendering a media contorl for image.

<?php
class Elementor_Test_Widget extends \Elementor\Widget_Base {

	protected function register_controls() {

		$this->start_controls_section(
			'section_content',
			[
				'label' => esc_html__( 'Content', 'textdomain' ),
				'tab' => \Elementor\Controls_Manager::TAB_CONTENT,
			]
		);

		$this->add_control(
			'image',
			[
				'label' => esc_html__( 'Choose Image', 'textdomain' ),
				'type' => \Elementor\Controls_Manager::MEDIA,
				'default' => [
					'url' => \Elementor\Utils::get_placeholder_image_src(),
				],
			]
		);

		$this->end_controls_section();

	}

	protected function render() {
		$settings = $this->get_settings_for_display();

		// Get image url
		echo '<img src="' . esc_url( $settings['image']['url'] ) . '" alt="">';

		// Get image by id
		echo wp_get_attachment_image( $settings['image']['id'], 'thumbnail' );
	}

	protected function content_template() {
		?>
		<img src="{{{ settings.image.url }}}">
		<?php
	}

}