How to hook in after user’s registration email has been sent?

I would use the registration_redirect filter. This allows you to set where the user is sent to, but leaves WordPress to perform the redirect (after everything has successfully processed).

function wpse_139267_registration_redirect( $url ) {
    return site_url( 'thank-you' );
}

add_filter( 'registration_redirect', 'wpse_139267_registration_redirect' );