How to set class to “current-page” on the currently viewed single post within a CPT

I figured it out.

Before the declaration of $case_query, I declare the active page id, like so: $active_page = get_the_ID();. Then, in the while loop after the_post(); I add the following:

$activeclass="";
if (get_the_ID() === $active_page) {
    $activeclass="current-page";
}

I also add the $activeclass to the .case-list-item div: <div class="case-list-item <?php echo $activeclass; ?>">

Solved.