The order overview is a very small overview of the complete order details page and with the limited space can only show a brief outline of the overall order. 

It is possible to add additional order buttons and integrations to the below section:

 

However it's not possible to add additional order information to the order overview outside of the above buttons. To add additional buttons to an order, please refer to the below guide with an example oh how to add a clickable button/link to an order:

How to add a clickable link to an order