Finn,

My heart goes out to you for I have been in a similar situation more than
once.  This is a tough one.  There are 3 conductors of the wiring harness
connected to the OXS: green (shielded), white and brown.  The green is the
signal to the ECU and should be connected to the black lead of your generic
OXS.  The white is the power supply for the resistive heating element of the
OXS and should be connected a white lead of the OXS.  The brown is the ground
for the heating element and should be connected to the other white lead of
the OXS.  I didn't realize it was possible, but it sounds like you took the
white conductor of the harness to ground through the OXS.

1/ Disconnect all the conductors to the OXS and briefly see how it runs.
2/ Check your wiring to see if you crossed the conductors.
3/ Check that either white lead of the OXS is not shorted to the body of the
OXS and that there is resistance between them.
4/ The white conductor from the harness is a real ballbuster because it comes
from a node WITHIN the wiring harness to which, by my count, 8 conductors are
terminated.  Also, it is fed directly from the battery through a relay.  In
other words, it is unfused.  Thank you VW!  Short of replacing the wiring
harness, you will have to at least strip the sheath back to assess the extent
of the damage.  Then, the relay and its wiring has to be checked.
5/ If, as I suspect, you swapped the leads to the OXS, you will have to
determine if the ECU was hardy enough for its input to be taken to ground
through the few Kohms of the OXS heater.

Rich