run sudo libinput-debug-events and check if the key press comes out of libinput. if it does this is likely a GNOME bug after all. It's not libinput itself that handles that key, we just forward it on.

I will provide you the information after a few hours, as the notebook is not nearby. What I noticed is, that every time when I press Fn + F8, on the screen I saw the notification that the touchpad is disabled, so I assume not the right key action is forwarded. Do you need any other logs except the debug-events information?

Are you under wayland or xorg? if you're under xorg, then check xinput list-props "... device name..." before/after and see if anything changes.

Also check the gsettings value before/after:
  gsettings get org.gnome.desktop.peripherals.touchpad send-events

those two should help narrow down where the issue is

I tried with both xorg and wayland and the result is just the same.
When I execute the following command :
gsettings set org.gnome.desktop.peripherals.touchpad send-events 'enabled'
it enables the touchpad. When I also try to play with the toggle button in Gnome settings, it disables/enables the touchpad as expected.

Ok, sounds like a GNOME issue then, because libinput doesn't know the difference between disabling through hotkey or the GUI, it's the same toggle. I'm closing this bug here, please file one in the gnome bugzilla instead.

Do check whether the key event is coming out of libinput first though, if not then it's a libinput bug after all (reopen if that's the case, but I doubt it)