Add a product tag to WooCommerce products via a custom cron job function

I have a custom cron job that automatically updates a pre-order product to 'out of stock' when it reaches a predefined date.

Is there a way I can also add a product tag to the product as part of this cron job?

Here's the code I have for the stock status update:

// Custom Cron hooked Function called by wp_schedule_event
add_action( 'jape_pre_order_stock_update', 'update_pre_order_stock_status' );
function update_pre_order_stock_status(){
    // Get all related product IDs to update via a WP_Query
    $products_ids = get_posts( [
        'post_type'     => 'product',
        'post_status'   => 'publish',
        'numberposts'   => 100, // <= the number of products to process (-1 is all)
        'fields'        => 'ids',
        'tax_query'     => array( array(
            'taxonomy'  => 'product_cat',
            'field'     => 'slug',
            'terms'     => array(
                'comic-book-pre-orders',
                'dc-comics-pre-orders',
                'image-comics-pre-orders',
                'manga-pre-orders',
                'marvel-comics-pre-orders',
                'other-publisher-pre-orders',
            ),
        ) ),
        'meta_query' => array( 
            'relation' => 'AND',
            array(
                'key'       => '_stock_status',
                'value'     => 'instock',
                'compare'   => '=',
            ),
            array(
                'key'       => 'woo_expiry_date',
                'value'     => date_i18n('Y-m-d'),
                'compare'   => '<=',
                'type'      => 'DATE',
            ),
            array(
                'key'       => 'woo_expiry_action',
                'value'     => 'out',
                'compare'   => '=',
            ),
        ),
    ] );

    foreach( $products_ids as $product_id ) {
        $product = wc_get_product($product_id);
        $shipping_class_id = 1002;

        $product->set_stock_quantity(0); // Set stock quantity
        $product->set_stock_status('outofstock'); // Set stock status
        $product->set_shipping_class_id( $shipping_class_id ); // Set the shipping class ID
        $product->save(); // Save updated product data
    }
    
    rocket_clean_post( $product );
    
}

I have this code for adding a tag when a product is sold out, but can't work out how to apply it to pre-orders in the cron job above:

// Add Out Of Stock tag to products when they sell out
function action_woocommerce_no_stock( $wc_get_product ) {
    // Get current tag id(s)
    $current_tag_ids = $wc_get_product->get_tag_ids();

    // Product set tag id(s), multiple IDs can be added, separated by a comma
    $new_tag_ids = array( '4074' );
    $wc_get_product->set_tag_ids( array_unique( array_merge( $current_tag_ids, $new_tag_ids ), SORT_REGULAR ) );

    // Save
    $wc_get_product->save();
}

add_action( 'woocommerce_no_stock', 'action_woocommerce_no_stock', 10, 1 );

Any suggestions would be very much appreciated!

Assuming that "4074" is the desired product tag term ID, simply use inside your products foreach loop, just before the save() method:

$product->set_tag_ids( array_unique( array_merge( $product->get_tag_ids(), [4074]) ) );

It should work.