[Azgoldrat]

My Corrado G60(factory Supercharged VW ) Started running lean at idle.
The FPR or fuel pressure regulator turned out to be the issue.
I had a 3 Bar FPR and changing to a 4 bar solved the issue.
Older injectors with the nozzles clogged up will also cause a poor spray pattern at idle with a supercharged engine causing Lean Condition.
If your system has a extra injector for over fueling then it is most likely used in the cold start/idle circuit also. Check the connection/harness there too.
Put a gauge on the Fuel rail and watch to see if the pressure drops out at idle.
My G60 was Stage III and put out 16-22 Lbs of Boost. on a 1.8L 20V, made EVO's Look Slow and stole the thunder from the Lightning. That little car was wAAY too much fun.
Hope it helps.
Az