A brief update about my car. It visited today a local Bosch Service (/ car electronics repair shop). That was nearly complete waste of time and money.
According to diagnosis crankshaft and camshaft sensors are OK, and ignition coils were getting OK signal. That was pretty much the most useful information I got.
In contrast to what I had asked, injectors had not been checked at all. Instead, I was told it is not possible to diagnose fuel injectors in any way. (This was not only opposite to what was told me on Friday when I was making the appointment, but also not really true, AFAIK.) Instead, the guy was suggesting they could swap(!) injectors of a misfiring and the non-misfiring cylinder. For some reason he had started working with some Corolla instead, leaving A2 half-open (air intake disconnected, etc) until I came to get it back. I guess this was actually a good thing.
Another suggestion I got was to get the ECU checked. It would take 2-3 weeks. If a problem was found, cost to fix it would typically be around 300-400€. Is anybody aware of such issues (misfire, poor idle) issues with FSI ECUs? If this is not a typical failure I'd assume it would be cheaper and easier to just get a new used ECU.
I was also informed that high-pressure fuel pump and camshaft failures are "typical" in "these engines" and could cause this kind of symptoms. Is this true? I don't remember reading about either of these issues.
I ended up paying 188€ for the visit. The mechanic was suggesting this was already a highly discounted price (because of their internal communication failures leading to a lacking work order, and that I was earlier "lied" about them being able to check injectors). I'm now thinking about making a complaint, although I'm not expecting to recover any money from this. I understand diagnosis work can be expensive, but it should be also carried out professionally and with somehow decent customer service.