How can I get alerted for out of stock items during order processing?

I don’t fully understand your flow but maybe you could turn off the product setting to allow selling when out of stock?

If not, if you need some kind of alert or action when an order gets marked paid, if you can’t find a native solution you can do stuff like this with Order Automator app. For example, you can make it send an email to staff when an order is marked paid and an item is out of stock. It’s not a stock feature but you can make customizations related to order automations.