Any resolution on this? Your photos look like there's seal leak on the air charge tube. This is not too uncommon & is fortunately is about as easy & cheap to fix on your own as it gets. Whether this is the cause of your apparent EGR issues, I can't say...

This air charge line is after the intercooler, & is pressurized under boost conditions. The oil residue is due to the crankcase ventilation system (CCV) putting oil mist & combustion blow-by from the crankcase into your air intake system (Seemingly, a chronic design issue for all BMW engines since the 1990's or so, both diesel & gasoline engines...)...

Pressure side air intake system leaks can cause a host of seemingly unrelated fault code SYMPTOMS & red herrings... The $160 diagnostic fee being asked by the dealership isn't unreasonable, as you can easily spend a whole lot more than that buying various replacement parts & sensors that are not actually faulty, let alone the value for your personal free time / sanity being used to replace all of the non-faulty parts...