functions.php

function dp_assign_post_year_term($post_id, $post, $update) {
	// Assign for new posts only
	if($update) {
		return;
	}
	
	// Assign only if post type is "post"
	if ( 'post' !== $post->post_type ) {
		return;
	}
	
    // Get the current year
    $current_year = date('Y');
	
	// Assign the post to the term in the "post_date" taxonomy with the current year
	$current_year_term_id = dp_check_create_term( $current_year, $post_id);
	
	if($current_year_term_id) {
		// Get the current Month
		$current_month = date('F');

		// Assign the post to the term in the "post_date" taxonomy with the current month
		$result = dp_check_create_term( $current_month, $post_id, $current_year_term_id, $current_year);
	}
    
}
add_action('save_post', 'dp_assign_post_year_term', 10, 3);

function dp_check_create_term($value, $post_id, $parent_term_id = null, $current_year = null) {
	$term = term_exists( $value, 'post_date', $parent_term_id);
	if( $term ) {
		// Term exists
		$existing_term_array = wp_set_post_terms( $post_id, $term['term_id'], 'post_date', true );
		if(!empty($existing_term_array) && is_array($existing_term_array)) {
			return $existing_term_array[0];
		}
	} else {
		// Create new term
		$args = [];
		if($parent_term_id) {
			$args = array(
				'parent' => $parent_term_id,
				'slug' => $value.'-'.$current_year,
			);
		}
		$new_term = wp_insert_term($value, 'post_date', $args);
		if( $new_term ) {
			$new_term_array = wp_set_post_terms( $post_id, $new_term['term_id'], 'post_date', true );
			if(!empty($new_term_array) && is_array($new_term_array)) {
				return $new_term_array[0];
			}
		}
	}
}