How to reproduce:

Connect the Xbox controller via Bluetooth
Create a new project with the “Universal 3D” template
Install the Input System package in the project
Open Window > Analysis > Input Debugger
Open the “Gamepad” device by double-clicking it
Press the left shoulder button on the controller
Observe the “Value” column

Actual result: Value is 1 in the row with the name “Select”
Expected result: Value is 1 in the row with the name “leftShoulder”

Reproducible with: 1.8.1 (6000.0.0f1), 1.19.0 (6000.5.0b12, 6000.6.0a7)

Reproducible on: Ubuntu 24.04.4 LTS (kernel 6.8.0-124-generic), other distributions tested by users with kernels 6.19.11-arch1-1 and 7.0.9-204.fc44
Not reproducible on: Windows 11

Workarounds:

Install the “xpadneo” Linux driver: https://github.com/atar-axis/xpadneo

Notes:

Tested on: Xbox Series S/X controller and the second version of the Xbox One S controller (the first version did not have a Bluetooth mode)
Does not reproduce with the wired USB connection
Have not tested with the Xbox One S controller wireless adapter
Might be a related to another known issue: https://issuetracker.unity3d.com/product/unity/issues/guid/UUM-136083
Updated the controller firmware to latest using the Windows 11 “Xbox Accessories” application