Automatically change order status if specific product is found within order.

functions.php

<?php
function custom_woocommerce_auto_complete_order( $order_id ) { 
    if ( ! $order_id ) {
        return;
    }

    $order = wc_get_order( $order_id );
    
    $product_ids   = array('12'); // Here set your targeted product(s) Id(s)
    $product_found = true;
    
    // Loop through order items
    foreach ( $order->get_items() as $item ) {
        if( ! array_intersect( $product_ids, array($item->get_product_id(), $item->get_variation_id()) ) ) {
            $product_found = false;
            break;
        }
    }

    if( $order->has_status( 'processing' ) && $product_found ) {
        $order->update_status( 'wc-arrival-shipment' );
    }
}
add_action( 'woocommerce_thankyou', 'custom_woocommerce_auto_complete_order' );