@Milo was absolutely correct…the issue was that I wasn’t getting a string to compare. The solution actually came from here.
What this ultimately looked like in my scenario:
<?php
if(has_term('dining-1', 'page_category', $post->ID)){
get_template_part('sidebar', 'dining-one');
}
elseif(has_term('dining-2', 'page_category', $post->ID)){
//etc.
}
?>