'In my Passat (with the AHU engine), they also overfilled it by about 1.5 cm. About 300 km later, the mass airflow sensor failed. I even noticed a decrease in performance just 30 km after the oil change.'
On my Passat, the crankcase ventilation hose connects to the intake hose about 10 cm away from the mass airflow sensor (MAF). I believe that the crankshaft is causing excessive oil to foam, and that this oil, which the ventilation system (likely overwhelmed by the amount of oil) can't fully separate, then reaches the MAF sensor.
Even though the LMM (likely referring to a lambda sensor) doesn't have a long lifespan anyway, the fact that it failed after such a short distance following the oil overfill strongly suggests that the overfill was the cause.
That's why the mechanic who changed the oil was also allowed to sponsor me a new MAF sensor

.
And a year later, my cat also broke down (at 65,000 km... which is a bit early, isn't it?).
Okay, so get the oil out immediately and contact the workshop right away to make sure they are responsible if the catalytic converter breaks down prematurely.
In my engine compartment, there are 2 warnings that the catalytic converter will fail due to oil overfilling... so, in reality, the workshop's license should be revoked immediately.

(and it's 2cm overfilled... that's almost 2 liters too much).