Thanks for the details, it seems that you reported this previously Manual paid plans and woocommerce orders not shown in Hivepress listings management so we’ll eventually fix this or find a workaround.
Please consider using online payment methods like Stripe or PayPal that would mark orders as Processing or Completed automatically. If there’s an offline payment method, WooCommerce should still send an email notification about a new order to the site admin (please check if this email is enabled in WooCommerce/Settings) so you can mark the order as Completed once you get a notification. Also, there may be a workaround if you change the order “Thank you” page, ensuring vendors that you’ll verify the payment as soon as possible.