There's no mystery here, so I didn't mention it in the write-up. The SoC has an LVDS output. The screen has a very long PCB with a specialised controller; it accepts LVDS and drives the pixels and backlight.

I think that the display is not used at all. If I understood correctly, the scart connector is hosting a hidden uart interface. This let's you connect a serial terminal via three cables. (You can e.g. buy a serial to usb adapter for 5 bucks on Amazon and use it via putt.)

You are correct. The SoC supposed to have a way to generate composite signal, according to the scarce data I found, but I didn't manage to force the board to do so. LVDS is (presumably) working, but I don't have any compatible LCD panels lying around.