Well, If I understand correctly, If unity can’t recognize the device, it will register it as a joystick and autogenerate a layout from its HID. I am not sure why there is a button missing from that HID but I would recommend to open the input debugger and see which buttons are registered in that layout.
Layouts can be represented using JSON and each button has certain characteristics, One of the most important ones are the bitoffset which tells unity which bit represent the button value. If you can’t find your buttons in the button layout, you can create your own custom layout and add your button, it might take some tinkering to find the button offset but you can try and guess by seeing the other buttons and their offsets
This is one of the main downsides for me in the new input system, I wish there was an easier way to map my device buttons to gamepads or create gamepad layouts for my joystick devices.
I would recommend reading this forum , it contains some helpful information