Show extra user profile meta for current user

You should use get_user_meta instead of get_the_author_meta(). because get_the_author_meta() has Valid values for the $field parameter include: get_the_author_meta

you can take reference from below code.

$school_id = get_user_meta( $current_user->ID, 'school-id',true);
if ( !empty($school_id) ) { ?>
    <p class="school-id">
        <p>
           <?php echo $school_id; # what you want to do with school id ?>
        </p>
    </p>
<?php }