hello again, problem found and (so far) solved! However, first, let's talk about troubleshooting. As the good tips above indicate, the intake valve is located in the middle of the engine, and the other one (when viewed from the front) is the throttle valve. What's unclear to me is why this (unlike other TDI engines) needs 2 similar valves in series. In between is only the introduction of the EGR (which I'll explain later). Since the A5 diagnostic process for the control unit is also selective (unlike the software in the B6/B7), it can be conveniently controlled, and you can then hear (of course, the engine must be turned off).
To access the intake valve, you must remove the entire intake pipe: 3 screws M6 T30 below the brackets/measuring pipe; one of them is barely visible and points upwards. And then the 4 long (5mm Allen key, M6), which go through the housing of the intake valve into the distributor. By the way: I always get a little nervous when I write about this intake pipe, especially since it's related to a turbocharged engine. These pipes don't actually suck in air (unlike the "turbo-free" intake diesel/petrol engine). Remove the two clips for the AGR and the fuel hose, as well as pull out the connectors of both valves.
Finally, loosen the screw under the cover to release the holder and "voilà", it's all done

. I have a size 10 glove, and I can't find my little wrench, so I'm a bit frustrated - but it still works somehow.
At first glance, everything was clear (see pictures): thick layers of soot in the pipe, valve, and distributor, up to almost 10 mm thick, and oily and greasy. It's a miracle that the valve was even able to function. And it had only 105,000 km on the odometer. I haven't seen this much soot in the AGR valve of my old 2.0 TDI before (those are notorious for it).
Further forensic investigations then showed that the AGR pipe is almost completely free. And this raises the suspicion that the problem is, once again, due to Audi's own design (as with so many others). Of course, some oil vapor always comes through the intake pipe, which was already the case with all TDI engines and should be known to Audi. Especially if you also suck the KG ventilation system with it. And I dare to say that, in this particular example, there is even less oil coming with the air compared to my two older cars and my previous Golf 3. This inevitably leads to oil and soot sticking directly after the intake of the AGR. I can imagine what it looks like inside the distributor itself. I strongly doubt that the airflow/distribution/turbulence is still functioning as it did on the test bench... I'm already relieved that the engine is still running. And I believe cleaning the distributor is almost impossible (possibly with ultrasound and sharp tools, etc.). Removing it would also be a major hassle. Or, this one produces significantly more soot instead of oil, likely due to frequent short trips. However, it should be able to. I could also imagine that the problem worsened after he received the Euro6 recall software update 2 years ago. Although it ran somewhat unevenly afterward, it wasn't really that bad before.
Okay, so far as possible cleaned and everything reassembled: The error is gone. Unfortunately, I now have error code P0133 (Lambda sensor value too slow). Perhaps something has become stuck. Hoping it will burn away
I would appreciate it if someone could share some more ideas for explaining the strong soot crust.