How to set featured image programmatically from url?

You can set an image as post featured thumbnail when it is in your media library. To add an image in your media library you need to upload it to your server.

try this code:

// Add Featured Image to Post
$image_url        = 'http://s.wordpress.org/style/images/wp-header-logo.png'; // Define the image URL here
$image_name       = 'wp-header-logo.png';
$upload_dir       = wp_upload_dir(); // Set upload folder
$image_data       = file_get_contents($image_url); // Get image data
$unique_file_name = wp_unique_filename( $upload_dir['path'], $image_name ); // Generate unique name
$filename         = basename( $unique_file_name ); // Create image file name

// Check folder permission and define file location
if( wp_mkdir_p( $upload_dir['path'] ) ) {
  $file = $upload_dir['path'] . '/' . $filename;
} else {
  $file = $upload_dir['basedir'] . '/' . $filename;
}

// Create the image  file on the server
file_put_contents( $file, $image_data );

// Check image file type
$wp_filetype = wp_check_filetype( $filename, null );

// Set attachment data
$attachment = array(
    'post_mime_type' => $wp_filetype['type'],
    'post_title'     => sanitize_file_name( $filename ),
    'post_content'   => '',
    'post_status'    => 'inherit'
);

// Create the attachment
$attach_id = wp_insert_attachment( $attachment, $file, $post_id );

// Include image.php
require_once(ABSPATH . 'wp-admin/includes/image.php');

// Define attachment metadata
$attach_data = wp_generate_attachment_metadata( $attach_id, $file );

// Assign metadata to attachment
wp_update_attachment_metadata( $attach_id, $attach_data );

// And finally assign featured image to post
set_post_thumbnail( $post_id, $attach_id );

ref url : http://www.wpexplorer.com/wordpress-featured-image-url/

Modified as your requirement: or that purpose ignore WordPress standard and upload your all post single image on your custom folder and add this image path or direct external image url into post as extra attribute meta field and when you will show post on your theme then just use your img with help of post id. demo code: for setting image

<?php
    update_post_meta ( 7, 'imgkey', 'www.url.path' );//7 is post id
?>

for getting image on your theme page where you want to show it

<?php
    $img_value = get_post_meta( get_the_ID(), 'imgkey', true );
?>
<img src="<?php echo $img_value?>">

Note if you are new in WordPress post custom meta fields then read this article: https://codex.wordpress.org/Custom_Fields
or
unofficial article about custom fields: https://premium.wpmudev.org/blog/creating-custom-fields-manually

if you have to load an image and then assign as thumbnail of the post, the quicker way is to use media_sideload_image and then set_post_thumbnail

https://developer.wordpress.org/reference/functions/media_sideload_image/

$url     = "http://url-of-the-image.jpg";
$post_id = [post id]
$desc    = "image description";

$image = media_sideload_image( $url, $post_id, $desc,'id' );

set_post_thumbnail( $post_id, $image );