I have installed Windows 10 and Ubuntu 20.04 on my HP Elitebook 850 G7, and in Ubuntu I noticed something strange. While, the touchpad in general works, the two extra buttons do not.
I found a lot of answers dealing with completely non-functioning touchpad, but in my case it's only the two extra buttons that do not work.
Below is some output of xinput. It lists two devices named SYNA30B4, which I suspect to be the touchpad and the extra buttons.
user@host:~$ xinput
⎡ Virtual core pointer id=2 [master pointer (3)]
⎜ ↳ Virtual core XTEST pointer id=4 [slave pointer (2)]
⎜ ↳ SYNA30B4:00 06CB:CE09 Mouse id=12 [slave pointer (2)]
⎜ ↳ SYNA30B4:00 06CB:CE09 Touchpad id=13 [slave pointer (2)]
⎜ ↳ Logitech USB Optical Mouse id=11 [slave pointer (2)]
⎣ Virtual core keyboard id=3 [master keyboard (2)]
↳ Virtual core XTEST keyboard id=5 [slave keyboard (3)]
↳ Power Button id=6 [slave keyboard (3)]
↳ Video Bus id=7 [slave keyboard (3)]
↳ Power Button id=8 [slave keyboard (3)]
↳ Sleep Button id=9 [slave keyboard (3)]
↳ HP HD Camera: HP HD Camera id=10 [slave keyboard (3)]
↳ Intel HID events id=14 [slave keyboard (3)]
↳ Intel HID 5 button array id=15 [slave keyboard (3)]
↳ AT Translated Set 2 keyboard id=16 [slave keyboard (3)]
↳ HP Wireless hotkeys id=17 [slave keyboard (3)]
↳ HP WMI hotkeys id=18 [slave keyboard (3)]
user@host:~$ xinput list-props 12
Device 'SYNA30B4:00 06CB:CE09 Mouse':
Device Enabled (174): 1
Coordinate Transformation Matrix (176): 1.000000, 0.000000, 0.000000, 0.000000, 1.000000, 0.000000, 0.000000, 0.000000, 1.000000
libinput Natural Scrolling Enabled (312): 0
libinput Natural Scrolling Enabled Default (313): 0
libinput Scroll Methods Available (314): 0, 0, 1
libinput Scroll Method Enabled (315): 0, 0, 1
libinput Scroll Method Enabled Default (316): 0, 0, 1
libinput Button Scrolling Button (317): 2
libinput Button Scrolling Button Default (318): 2
libinput Middle Emulation Enabled (319): 0
libinput Middle Emulation Enabled Default (320): 0
libinput Accel Speed (321): 0.000000
libinput Accel Speed Default (322): 0.000000
libinput Accel Profiles Available (323): 1, 1
libinput Accel Profile Enabled (324): 1, 0
libinput Accel Profile Enabled Default (325): 1, 0
libinput Left Handed Enabled (326): 0
libinput Left Handed Enabled Default (327): 0
libinput Send Events Modes Available (297): 1, 0
libinput Send Events Mode Enabled (298): 0, 0
libinput Send Events Mode Enabled Default (299): 0, 0
Device Node (300): "/dev/input/event12"
Device Product ID (301): 1739, 52745
libinput Drag Lock Buttons (328): <no items>
libinput Horizontal Scroll Enabled (329): 1
user@host:~$ xinput list-props 13
Device 'SYNA30B4:00 06CB:CE09 Touchpad':
Device Enabled (174): 1
Coordinate Transformation Matrix (176): 1.000000, 0.000000, 0.000000, 0.000000, 1.000000, 0.000000, 0.000000, 0.000000, 1.000000
libinput Tapping Enabled (330): 1
libinput Tapping Enabled Default (331): 0
libinput Tapping Drag Enabled (332): 1
libinput Tapping Drag Enabled Default (333): 1
libinput Tapping Drag Lock Enabled (334): 0
libinput Tapping Drag Lock Enabled Default (335): 0
libinput Tapping Button Mapping Enabled (336): 1, 0
libinput Tapping Button Mapping Default (337): 1, 0
libinput Natural Scrolling Enabled (312): 0
libinput Natural Scrolling Enabled Default (313): 0
libinput Disable While Typing Enabled (338): 1
libinput Disable While Typing Enabled Default (339): 1
libinput Scroll Methods Available (314): 1, 1, 0
libinput Scroll Method Enabled (315): 1, 0, 0
libinput Scroll Method Enabled Default (316): 1, 0, 0
libinput Click Methods Available (340): 1, 1
libinput Click Method Enabled (341): 1, 0
libinput Click Method Enabled Default (342): 1, 0
libinput Middle Emulation Enabled (319): 0
libinput Middle Emulation Enabled Default (320): 0
libinput Accel Speed (321): 0.000000
libinput Accel Speed Default (322): 0.000000
libinput Left Handed Enabled (326): 0
libinput Left Handed Enabled Default (327): 0
libinput Send Events Modes Available (297): 1, 1
libinput Send Events Mode Enabled (298): 0, 0
libinput Send Events Mode Enabled Default (299): 0, 0
Device Node (300): "/dev/input/event13"
Device Product ID (301): 1739, 52745
libinput Drag Lock Buttons (328): <no items>
libinput Horizontal Scroll Enabled (329): 1
user@host:~$ xinput list-props 15
Device 'Intel HID 5 button array':
Device Enabled (174): 1
Coordinate Transformation Matrix (176): 1.000000, 0.000000, 0.000000, 0.000000, 1.000000, 0.000000, 0.000000, 0.000000, 1.000000
libinput Send Events Modes Available (297): 1, 0
libinput Send Events Mode Enabled (298): 0, 0
libinput Send Events Mode Enabled Default (299): 0, 0
Device Node (300): "/dev/input/event9"
Device Product ID (301): 0, 0
user@host:~$
I have solved the issue with a more recent Linux kernel.
The issue has already been resolved in the Linux 5.10 kernel. However, my initial installation featured the linux-oem-20.04 kernel package. This package is based on the Linux 5.6.* kernel.
I have changed to the linux-oem-20.04b kernel package, which is based on the Linux 5.10 kernel. After installing the new kernel package, and rebooting, the trackpad buttons work as expected.