Sounds like you might have a leaking injector or injector that is stuck open on cylinder 2.
The early EA888 engines are known for carbon buildup, and yes the carbon buildup can cause misifires but its usually on idle and low throttle inputs only. When they take the inlet manifold off to clean it, they may as well replace at least injector #2 while they are there as they will have perfect access to it.
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