BTW I am also using a Lenovo ThinkPad Trackpoint Keyboard II, I have the wireless one, using it in bluetooth in both Windows 11 and Linux without problem, everything works.
Can you share a photo of it? Here is my one: I could not get it to work on Win 11 so I downgraded to Win 10. Which feels less bloated... But I am having the speakers fail AGAIN.
I have the "Thinkpad Trackpoint Keyboard II" which is a little bit different. I paired it in Windows 11, then in Linux I extracted the pairing key to use the same, so in bluetooth mode it works in windows/linux