HID with bidirectional communication I want to build a gamepad HID using the Arduino Micro, and intend to use Nico’s HID library for that.

But I would like to send some config info from the PC to the Arduino HID as well.

Can you have a gamepad that not only sends state to the PC, but also receives a configuration from the PC?

I intend to use this with a Linux PC as host.
Yes, but the configuration side of things will not be part of the gamepad HID.  You will need to set up a second communication channel - be that serial or raw HID - to do the configuration.