Craftsman damages front door - How is he liable?

Uhm, actually yes. He does not deny having caused the damage, but he does dispute the amount of the damage and thus the claim. Therefore, the claim is not fully effective. It would only be so with a title.

My "gut feeling" agrees with , nevertheless the pragmatic way might be to pay (a reasonable) amount in order to settle the repair. Who would sue over such amounts right away? And will the craftsman (assuming sufficient reasonableness) not eventually see this and simply settle with his insurance? Provided sufficiently calm and factual communication. It does not fit 100% perfectly, but "If you want peace, prepare for war."

For such things, the craftsman should have liability insurance.

with a 1000.-- deductible. I had water damage, the insurance immediately paid 100.-- and the rest only after many reminders weeks later from the craftsman

But that's actually not how the deductible works. Actually, the insurance settles immediately and recovers the deductible from the insured.

We had a similar case. The door was damaged shortly before the handover of the house, most likely by the cleaning crew, on the frame and the wooden door itself. It resulted in a complete replacement of the door, as the scratch could not be repaired. The frame was repaired and the wooden door was replaced. It took about 3 months because the door was a custom-made piece. The invoice was then settled by the construction company through their liability insurance. I just forwarded the invoice. It was therefore handled smoothly by the construction company.