Warning: Undefined variable $post_id

Try this instead:

$posts_with_category = new WP_Query( $args );

if( $posts_with_category->have_posts() ) {

Instead of just checking if $posts_with_category is non-empty it checks if it’s an array of WP_Post objects.

We don’t have line numbers to see where the error is being thrown. Is line 47 your return statement?

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