Hi,
First, can you check the orders ? Is their status being changed to "confirmed" automatically after the payment ?
That's the condition for the invoice number to be generated.
If that doesn't happen, then the problem is with the payment method. For example, some payment gateways require that you provide the callback URL in your merchant account on their website. And thus, if you migrate, you might need to update that information.
You say that the invoice numbers were not generated anymore after updating the PDF invoice plugin. So, supposing that the PDF invoice plugin caused this, disabling it in the Joomla plugins manager should fix the invoice number generation. Can you test this ?
What if you manually change the status of an order from created to confirmed in the backend, do you get the invoice number generated ? Do you see an error message ? Which one ?