Find all posts in converted categories and threads and add a "projects" category to them.

projects-cat-to-converted.php

<?php

function akv3_add_projects_cat() {
	// find all posts in converted categories and threads
	$term_ids = array(400, 417, 438, 455, 13, 14, 15, 20, 22, 52, 53, 58, 59);
	$query = new WP_Query(array(
		'posts_per_page' => -1,
		'tax_query' => array(
			array(
				'taxonomy' => 'projects',
				'field' => 'id',
				'terms' => $term_ids,
				'operator' => 'IN'
			)
		)
	));
	// add "projects" cat to those posts
	foreach ($query->posts as $post) {
		wp_set_object_terms($post->ID, 'projects', 'category', true);
	}
}