How to edit the new user email notification template

This is done with the register_new_user filter:

// Replace the default new user notification
remove_action('register_new_user', 'wp_send_new_user_notifications');
add_action('register_new_user', 'my_new_user_email');

You have to remove the default action and register the new function:

Create a new function that builds and sends the message.

function my_new_user_email($user_id, $deprecated = null, $notify = 'user') {
   // create the message
    $message = "Hello new user!";

    // Send the email
    wp_mail(get_userdata($user_id)->user_email, 'Custom Subject', $message);
}

This is placed in the functions.php file of your Child Theme (not the main theme, as any theme update will overwrite your changes).

Make the desired changes to the message text. Add headers to allow for an HTML message. (Lots of googles/bings/ducks on how to do that.)