The screen is connected to the motherboard or mainboard with an eDP (embedded DisplayPort)
Nirav has already found a cool little usb-c to 40-pin eDP that works fine, recognizing the screen and outputting the right resolution!
(The post can be found here)
If you’re intrigued, the board is available on aliexpress.
It would be cool to see a case designed where the old display is mounted on top of the new one in some jank way with an eDP extension cable because it is rather short. Maybe a way to have the small board integrated in some expansion card?