Chosen Solution
Update (07/25/2022) I successfully repaired the display! The problem was the All-in-one-cable. I suspected the cable after visually inspecting the PSU and logic board, which looked fine. I also measured correct voltages coming from the PSU, and also seeing that the logic board spun up the fan, so it seemed to be at least somewhat functional. The AIO cable was 25 EUR from eBay and the display now works perfectly!
In a darkened room when you turn on the display do you see a bit of a glow? If you do that is telling us the backlight is powering up. If not then I’m suspecting you have a power supply issue as this display has two power feeds 3.3 V DC & 5.1 V DC its possible one has failed. Google: LED Cinema Display 27" (A1316) Apple Technicians Guide Which is similar to the Thunderbolt display and can be found.
