Is the dealership trying to scam me out of my warranty?

On July 23rd of this year, I bought (financed) a used car for about $11k from the used sales department at a Chevrolet dealership in my town. I put down $3k. Everything felt fine whenever I was test driving the car, but upon driving it in the real world up and down hills and what not I noticed a shudder in the transmission between first and second gear. I immediately let the salesman know, because I made sure to receive a 30 day dealer warranty since I’ve had bad experiences in the past with used cars. This was a pretty big topic of conversation for us before I bought the car. So I sent him a message and let him know what was going on with the car immediately and I brought it back up to the service center the following day to get inspected. Well, they sent me a quote two days later for over $7000 for a new transmission. I immediately called the sales rep for further information because it said it was pending approval. She said she had to check with sales to make sure they would cover this repair. For anyone wondering, I had the 1000 miles/30 day dealer warranty with a $99 deductible. Well, ever since the service rep told me she would have to check with sales, I haven’t been able to get back in touch with her and everyone has been giving me the runaround about when I will get an update. I finally got in touch with the Salesman today, and he told me the manager above all of them is doing an investigation as to why the car was sold to me with a bad transmission in the first place.

A key part of the story is the finance guy talked me into an extended warranty that sounded like a no-brainer at the time, until I received my welcome letter in the mail showing that it’s actually costing me over $4300. I immediately went back up there and told him I want to cancel it and he told me I would have to wait until my first bill comes before I can cancel it - with the warranty company directly.

Now that the car is actually having a major mechanical issue though, the salesman told me today that they are likely going to try to put this on the extended warranty set up on themselves because they would be “taking a loss” and no dealership is going to want to do that. He’s putting the blame on “them” whoever that is, as if he separate from the dealership LOL. I’m pretty confused, this was obviously a pre-existing condition with the car. Is there anyway the dealership can get out of this? What should my next step be to make sure I don’t get screwed over, whenever I intended canceling the extended warranty ASAP. I don’t understand why they are making it seem like they have a choice, whether they are going to as if the warranty is not legally binding document. Someone help. Should I contact the extended warranty company and let them know what the dealership is trying to pull over on them? Before my 30 day dealer warranty is up in this becomes an even bigger issue?