Hi Daniel, I hope you're doing well!
The USART interrupt example you took for reference should be able to help you get an idea on how to implement a USART module to communicate with your QN9080. The implementation can be integrated into the private_profile_client.c source file.
An alternative way of setting up an UART module for projects using the BLE stack is with the Serial Manager API. The Private Profile Client SDK example already uses the Serial Manager to set-up a UART in this example.
A guide on how to enable an additional Serial Manager instance can be found here. The example uses an I2C interface instead of UART, and it uses KW41Z, but the process is more or less the same.
Please let me know if you need any more information.
Best regards,
Sebastian