How to reproduce:
1. Create and open a new HDRP project
2. Open Window → Package Manager -> Package Manager → Unity Registry
3. Install the Input System package
4. Open Window → Analysis → Input Debugger
5. Double-click the mouse icon
6. Try pressing the mouse forward and back buttons
7. Observe the “Value” column in the backButton and ForwardButton rows

Expected result: backButton or forwardButton “Value“ changes to 1 when the buttons are pressed
Actual result: backButton or forwardButton “Value“ remains 0 regardless of whether the buttons are pressed or not

Reproducible with: 0.2.10-preview (2023.1.0a4, 6000.0.62f1, 6000.2.11f1, 6000.3.0b9, 6000.4.0a4), 1.15.0 (6000.0.62f1, 6000.2.11f1, 6000.3.0b9, 6000.4.0a4)

Reproducible on: Ubuntu 22.04
Not reproducible on: Windows 11

Update: 

Important note. While testing we noticed inconsistent behavior with some mice. We determined that this is not OS or driver specific but rather a peculiarity of the mouse.

For example with the mice we have tested with.

A 2013 Razer DeathAdder behave as you would expect. Hold the button down and you see the value in the Input debugger goes to 1. Release and it goes to 0. Great!

The Logitech MX Anywhere 3 coalesces both the press and release events and send them upon the buttons release. So in the debugger you see a quick flip to 1 then back to 0.