Hi Leo, thank you. This worked, for anyone who might need it in the future (I adjusted the code that was hiding the website input):
add_filter( 'comment_form_default_fields', function( $fields ) {
$commenter = wp_get_current_commenter();
$consent = empty( $commenter['comment_author_email'] ) ? '' : ' checked="checked"';
$fields['cookies'] = '<p class="comment-form-cookies-consent"><input id="wp-comment-cookies-consent" name="wp-comment-cookies-consent" type="checkbox" checked="checked" value="yes"' . $consent . ' />' . '<label for="wp-comment-cookies-consent">Save my name and email in this browser for the next time I comment.</label></p>';
return $fields;
}, 20 );