Update:
Since my car still has a worldwide warranty, and I obviously wanted to handle it through that, I went straight to the VW service center here in Graz on Wednesday.
Okay, I accepted the offer, explained the problem, and left the car there. Then, just to be safe and to inform him beforehand, I contacted the salesperson who connected me with the car.
The car was ready on Thursday... the sensor was replaced, the DPF was regenerated... AND:
MSTG updated to software version 4356!
I've already driven about 300 km, but I haven't been able to notice any real differences yet, neither in fuel consumption nor in top speed. I need to drive a bit further to see any significant changes!
Regarding acceleration, I can say that it sometimes feels a little "gentler." It feels like the turbo boost builds up a moment later/slower, especially during kick-down situations on the highway. I even experienced a noticeable jerk once when shifting from 6th to 4th gear during a kick-down. However, that's been the only thing I've noticed so far!
He's likely very close to achieving top performance... I'd be happy to create some logs if anyone is considering doing such an update, or simply wants to know where the actual differences lie.
The shifting problem has largely subsided, although it still seems a little slower to me (probably very subjectively) than it was before the exhaust system warning light came on!
So much from my side... if anyone would like to compare logs, I'd be happy to help - if there's any need for it

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Thank you, and best regards from Austria.
Alex.