How to get image URL from media_sideload_image?

Try the fourth input parameter (available in 4.2+):

@param string $return  
       Optional. Accepts 'html' (image tag html) or "https://wordpress.stackexchange.com/questions/212512/src" (URL). Default 'html'.

So change your code snippet to:

$new_image_url = media_sideload_image($new_url, $post_ID, $title, $src="https://wordpress.stackexchange.com/questions/212512/src" );

to get the src instead of the default html.

Note that the output might also be an WP_Error object for errors, so you might add a check for that.