Accident with VW truck – what’s coming to me?

Hello guys, since my golf is being upgraded to car gas at my VW dealer at the moment, it was nice to borrow a Lupo as a replacement. Last night, unfortunately, something stupid happened to me with this car. I hit a big stone on a green strip next to the road in the semi-darkness. I turn around with the golf almost every day and there was never such a chunk around. I could bite my ass like that. There I drive for years without the tiniest Parkrampler and there What I saw yesterday with the flashlight didn’t look good. The lower unpainted part of the bumper is pressed in at the left corner and also from the lacquered upper part a small piece is broken off at the edge to the unpainted part, which is hardly noticeable. I was able to push the dent out again with my hand, but in the plastic there are still clearly the scratches and a pinch to be seen. The only positive thing is that the painted part didn’t get anything except for the small corner. (perhaps stuck and right on the car) I can’t even assess what the repair would cost. Now to my questions: I got the rental car without any signature. VW wanted only a copy of the driver’s license. In such a moment you don’t think of anything like that. I just know that the car is probably also rented for EuroMobil. . I realize that I screwed it up myself, but what about the insurance cover here? Are such cars fully casco-insurance? Do I possibly take over my own private liability? Was one of you ever in such a situation? The car is so capable of driving and I don’t know when my golf will be finished. So I have another day, two days, until I have to confess the damage at VW. Or should I rather go to VW immediately? I don’t want to do it myself. It’s a small car dealership and I’ve always been good with them. It’s kind of embarrassing to me, to be honest. Thanks for reading and for your tips! Robert