Brightness keys not working in Linux

[Eckstein]

Setup: HP EliteBook x360 1030 G4; Dual boot with Windows 10 with most recent updates from Microsoft and HP (as suggested in the according programs), (latest) BIOS Rev94 01.04.02 and Ubuntu 18.04 (and kernel 5.5.11).
Issue: Brightness up/down keys (f3/f4) are not working in Ubuntu/Linux - they produce the same scan codes as MicrophoneMute (f8).
Observation: After BIOS flash (with same version) the keys work as expected over reboot as well as power down/up cycles. Booting into Windows and then into Linux again, causes the Issue to reappear and persist until BIOS (re)flash.
Presumption: Windows drivers (main suspect: HP Hotkey Support) change settings in the keyboard controller, persistent over reboots. BIOS does not reset these to the initial sate.
Possible mitigation: Change Windows driver(s) for not corrupting keyboard behavior; change BIOS for resetting keyboard settings or not storing the changes over reboots; Provide information on the needed keyboard initialization to be introduced into Linux.
Any suggestion will be appreciated.

[WAWood]

@Eckstein 

Sorry, but the Linux keys problem is due to the lack of drivers and HP does not supply Linux drivers.

You would have to check the Ubuntu Forums to see if anyone there has any such drivers.

[Eckstein]

Thank you for the reply.

Yes, the Linux keys problem is related to Linux and might be resolved by an appropriate Linux driver.

And no, it is not just an issue in Linux, as the combination of Windows drivers and BIOS (implementation?) causes the strange behavior, described in my first post.

Especially the fact that everything works as expected in Linux (using the drivers available in Linux) after flashing the BIOS indicates some unusual (to say the least) behavior. Working as expected until Windows is booted, that is.

After checking of feeling like thousands of Linux forum entries, some of which also reporting solving the issue after BIOS updates but none with reappearing after Windows boot, I end up here, hoping for hints on Windows driver information, or documentation, that could lead to further development on the Linux side to work around this strange behavior.

In case, there is an HP Community area, dealing with Linux issues, where this question will be more appropriate, I am sorry for bothering you and not finding that one...

[Eckstein]

No solution - an unsatisfying workaround, though:

Uninstalled the HP Hotkey support in Windows (disable the Hotkey service), flash the BIOS again, and Windows does not change the keyboard settings any more; the brightness keys work in Linux as expected. They do not work in Windows, though.

Thus, I can decide, in which operating system the brightness keys shall work - Windows or Linux - and enable/disable the Hotkey service in Windows accordingly.

I still find the behavior of changing (some of) the BIOS settings by a driver rather uncommon and strange - problematic in any case.