As I stated in an earlier post in this thread, I've never seen a BHW clogged up an exhaust. However, ruling it out is probably wise at this stage.
He did say the car sat... for all we know, a troop of chipmunks made a nest in the muffler in that time. Who knows, stranger things have happened.
He may have said this, but I'm still not clear on it, if the car has full power with the intake flap/EGR unplugged or not. Sounds like it does not.
A clogged exhaust would:
Cause low power, especially the faster the engine spins.
Cause high exhaust backpressure, which would mean far more EGR flow than intended, which would cause poor combustion, and thus low power.
The ECU will run the engine perfectly fine with both the intake throttle flap and EGR unplugged. A stock engine with those items disconnected will still be capable of making 100% of its maximum power. Because even with those items working, they'd both be in the same position as they would be unplugged if the ECU commanded full power anyway.
So if those items are off the table, and the engine STILL cannot make full power, then it would be narrowed down to some sort of air flow restriction (may not even be in the exhaust, for that matter, could be the intake or charge air tract), or severe underfueling. I have seen low power from severe underfueling in VE TDIs from incorrectly stored injectors... and they will start and run and idle perfectly fine. Smooth idle numbers will even be good, amazingly. But they will barely get out of their own way. And no DTCs at all. The only "clue" I ever got with those, was the oil was still whistle-dick clean, and in both cases, it was fortunate that the engines had just been put back together and fresh oil was in there. Otherwise I may not have realized what was going on. Once the injectors were remedied, the engine(s) ran great, and the oil was normal black within a few miles.