Finally it is done!

I paid a deductible, of 2000kr (~�180, �210) and the insurance covered the rest, ECU, lockset etc.

Total cost without the insurance coverage would have been around 15000kr, (~�1380, �1575).
They covered the other bike too, which I still had the red key. So I will get a new key, reprogramming and a disk brake lock without paying a deductible for the other bike, which was nice.