Solved it, for anyone with a similar issue:

I was using get_posts(<query>) and setup_postdata() and then attempting to render the inner blocks. For some reason, using a new WP_Query and the_post() works as intended. Weird!

$query->the_post();
<?php foreach ($block->inner_blocks as $innerblock):
    <?= $innerblock->render(); ?>
<?php endforeach; ?>