Extra headers like ‘List-Unsubscribe’ is not a function of the email server (exim4) but of the sending software. Ex: See php mail function here or PHPMailer library here
Furthermore I’ve found an old post about Exim… https://saeedrahhal.wordpress.com/tag/exim/ where the author says to setup the “headers_add” directive in Exim’s config file (but unfortunately Exim has several config files…)