I would put my money on the PCV valve. Before I had my own VCDS my engine ran badly at idle and low throttle. A new valve cured it. At that time I was very much an EOS beginner but a retired mechanic friend had come across this issue on Golf GTIs having the same engine. He had a known good valve in his shed and we changed it . It worked! Not very scientific I know and I suggest you don't discount the possibility of other faults but it could be an inexpensive fix?
2006(06) 2.0T FSI Sport manual.