opens like sitename.com/URL

sgdghd.com is not a complete URL on its own, and if used in a link like <a href="https://wordpress.stackexchange.com/questions/358412/sgdghd.com">, it will be treated as a relative URL. To properly link to a different domain, you need to include http:// or https://.

To ensure that a value for href is a valid URL, you should use esc_url() when outputting it. That way if a user enters an incomplete URL in the settings, it will still be output correctly:

echo '<a href="';

echo esc_url( $settings['url'] );

echo '">';