I searched every corner of the options there but I can't figure out what you mean
I just checked and you are right, it's possible to enable/disable Steam input for external controllers, but not for the built-in controller.
Our game uses "Gamepad with joystick trackpad" template. And like I said, all buttons work correctly - Left/Right trigger and shoulder buttons.
We are using NWJS Linux64 export and the compatibility mode on Steam Deck is disabled.