Payment without prior assessment

Hello together! I’m new here and had to register because I just experienced something I had never experienced before. I ordered a new car on condition that the corresponding car dealership takes my car into payment. Said: New car ordered (leasing) and the nice salesman promised me the payment amount orally. (At this time I was already the third time there and also every time with my vehicle) Now came the day and my new car wur So far the nice salesman has not looked at or had my “old” vehicle checked. We signed all the papers and also fixed the purchase of my car for the promised amount. The sales said “so now we walk around the car and look at the car” said. He meant the car is super there and the purchase was signed. I left papers and keys right there because it will be logged off the next day. The car was still in a financing and was therefore triggered by the car dealership and “taken over”. I left the old one right there and drove with my new one from the yard. The next day the seller called me and said that my air conditioning system did not work and they did not know what it was about (Important: I had no idea that this was not working, the car was cared for and had only a replacement in the contract workshop). He would run me on the run. But if it’s a bigger thing, I have to come up for the reperture. Now the question I’m asking myself: Can the car dealership claim against me in some way? I’m really surprised that the seller didn’t have the car checked before “purchase” and now after processing/purchase the workshop looks over it and thinks it’s a little defective and I have to pay for it. I’ve never heard anything like this, especially not in case of a lack of the I cannot know myself. I would be grateful for any help as I am really surprised. Thank you and greetings