Hi @a95web,
Nice troubleshooting on this already!
Yes, I believe you’ve found the issue. Emails for paid orders won’t be sent if the order is still in Pending payment status. Note that here in our email FAQ: Check if orders are pending
You can test this theory by adjusting a paid order that’s still in Pending to Processing and checking that the email is sent.
You shouldn’t usually need a code to change order status to Processing once it is paid. The status should be updated by your payment gateway. I’d recommend seeing why the gateway isn’t setting orders as Processing once they are paid. Solve this, and your email issue will likely be solved as well.