why does get_option( ‘home’ ) not work while using in plugin [closed]

get_option() returns a string, it doesn’t print anything. You have to use echo or print.

But you should use home_url() instead, because this takes care of the proper scheme (http or https):

echo esc_url( home_url() );

Or, in case of the log in URL:

echo esc_url( wp_login_url() );